Here's the moment she did it:
And next up for Konta is a semi-final at 2am on Friday morning against either world No 1 Angelique Kerber or the legendary Venus Williams.
Game, set and match! Konta defeats Halep 3-6, 7-6, 6-2
Halep remember served for the match in the second set, and was two points away from pulling it off. Now, just over an hour later it's Konta who is serving for a place in the semi-final. Can she succeed where Halep so spectacularly failed?
The players exchange errors on the first two points, before Halep sends a backhand wide for 30-15. Joko though pushes a backhand long, and it's 30-30. Halep then puts a forehand long to gift Konta a match point at 40-30, and another long Halep forehand seals the win for Konta!
Game, set and match.
Konta* 3-6, 7-6, 5-2 Halep (*denotes next server) - Konta breaks and will serve for the match
Halep looks a bit as though she's checking out mentally, as Konta keeps her focus to flick away an angled forehand volley for 15-30. Halep then nets a backhand for 30-40 and JoKo has a break point that if she takes would leave her serving for the match. She can't take it though, snatching at a forehand return and sending it long. No matter though, Halep gifts Konta a second break point with a missed forehand, and another error hands the Brit the break. She will now serve for the match.
Konta 3-6, 7-6, 4-2 Halep* (*denotes next server)
Bruising hitting from JoKo, and she's starting to overpower Halep a little. A bullet forehand makes it 30-0 before a brilliant drive volley sets up 40-15. Halep then nets a forehand to 15, and Konta consolidates the break with a comfortable hold to 15.
Konta* 3-6, 7-6, 3-2 Halep (*denotes next server) - Konta breaks!
Konta all over Halep's second serve at the moment, and she flicks a way a forehand winner return to make it 30-30. A strong return off the same wing earns Konta a break point at 30-40, and she takes it when Halep sends a forehand long! The Brit is now just three games away from a place in the semi-final.
Konta 3-6, 7-6, 2-2 Halep* (*denotes next server)
The match enters its third hour, and we're still no closer to knowing who will win this match. Halep though has a glimmer of a break at 30-30, earned with a thumped forehand winner down the line. JoKo responds though with two excellent backhand volleys to earn the hold and level the second set.
Konta* 3-6, 7-6, 1-2 Halep (*denotes next server)
Konta is doing the right things and trying to be aggressive, but she's just making too many errors at the moment. A few more this game gift Halep a gratefully received love hold.
Konta 3-6, 7-6, 1-1 Halep* (*denotes next server)
Konta deals well with the disappointment of missing those break points and completes a hold to 15 with a brilliant forehand down the line after some strong serving.
Konta* 3-6, 7-6, 0-1 Halep (*denotes next server) - Halep saves four break points and holds!
Halep needs to shake herself out of this, and somehow she does just that, fending off four break points to hold serve. Konta really needs to start converting more of these break points.
Halep not happy
Halep is an almighty funk at the moment, seeing the negatives in just about everything and venting at her coach Darren Cahill, who is on court following the end of the second set.
"You're a better athlete than what she is," Cahill says to Halep, but she really doesn't want to listen to anything he says. He's pretty much there as a punchbag - similar to the fourth official in football.
Konta 3-6, 7-6 Halep* (*denotes next server) - Game and second set Konta!
Halep nets a forehand and it's Konta who nicks the breaker 9-7. We're into a deciding set!
Tie-break: Konta* 8-7 Halep (*denotes next server) - Set point Konta
Halep with a moonball forehand that flies long, and it's a third set point for Konta.
Tie-break: Konta 7-7 Halep* (*denotes next server)
Konta chucks in another forehand error and the chance goes begging.
Tie-break: Konta 7-6 Halep* (*denotes next server) - Set point Konta
Brilliant serve and backhand winner combo brings up a second set point for Konta.
Tie-break: Konta* 6-6 Halep (*denotes next server)
This really has been one of the edgiest tie-breaks you could ever hope to see, and Konta can't hold her nerve, pushing a forehand long for 6-6.
Tie-break: Konta* 6-5 Halep (*denotes next server) - Set point Konta!
Halep sprays a forehand long, and it's set point Konta!
Tie-break: Konta 5-5 Halep* (*denotes next server)
A Halep backhand clips the tape, setting up an easy forehand winner for Konta. We're back on level terms.
Tie-break: Konta 4-5 Halep* (*denotes next server)
A gutsy second serve from Konta, and she earns her reward when Halep sends a backhand long. The Romanian now has two points on her serve to win the match.
Tie-break: Konta* 3-5 Halep (*denotes next server)
Konta pushes a forehand long and Halep is just two points away from the win.
Tie-break: Konta* 3-4 Halep (*denotes next server)
At last a point is won by the server, as Halep outlasts Konta and forces her to send a forehand long after a bruising exchange.
Tie-break: Konta 3-3 Halep* (*denotes next server)
Oh my word, Halep chucks in another double fault. This is desperately tense.
Tie-break: Konta 2-3 Halep* (*denotes next server)
Konta sends a backhand long, and the advantage swings back the Romanian's way.
Tie-break: Konta* 2-2 Halep (*denotes next server)
Good serve from Konta but a brilliant Halep return forces the Brit to send a forehand well long. Every point has gone against the server so far.
Tie-break: Konta* 2-1 Halep (*denotes next server)
Halep chucks in her sixth double fault of the match to fall down a mini-break.
Tie-break: Konta 1-1 Halep* (*denotes next server)
A Konta forehand winner up the line instantly wrestles the mini-break back and levels it at 1-1.
Tie-break: Konta 0-1 Halep* (*denotes next server)
A double fault from Konta gets her off to the worst possible start.
Konta* 3-6, 6-6 Halep (*denotes next server) - Tie-break time
An ace, a forehand winner, and a missed Konta forehand take Halep to 40-0. Another ace then wraps up a hold to 15, and we're into a tie-break.
Konta 3-6, 6-5 Halep* (*denotes next server) - Konta saves a break point and holds
Both players are really struggling on their serves, and Halep forces 30-30 with a wonderfully crisp backhand return. She then forces a break point with a wrong-footing crosscourt forehand winner, but makes a mess of it with a shanked forehand that flies well long. Konta grits her teeth and takes the next two points to complete the hold, and put the pressure right back on her opponent.
Halep is really feeling the considerable Miami heat right now.
Konta* 3-6, 5-5 Halep (*denotes next server) - Konta breaks back!
That is precisely how not to start a game when you're serving for the match - a double fault. Konta though chucks in an error of her own on the next point to make it 15-15, and she then opts for a strange forehand slice which goes horribly wrong for 30-15. But the Brit responds well to make it 30-30 with a feather-light half-volley pick-up, and a long Halep forehand gifts her a break point at 30-40. Can she take one of these at last? No! Again Konta is tentative with a forehand volley and she is punished by a glorious Halep lob. An inopportune double fault then hands Konta another break point, but again she misses a sitter, sending a simple forehand return way long. But finally it's third time lucky as Konta earns another break point with a big forehand and then takes it when the Romanian send a backhand wide.
Phew, big relief for Konta, and you'd have to say Halep really tightened up there. She looks furious with herself and coach Darren Cahill.
Konta 3-6, 4-5 Halep* (*denotes next server) - Halep breaks and will serve for the match
Oh dear, a Konta double fault has her down 15-30 and in danger of what would be a potentially fatal break of serve. Halpe senses this could be the moment, and forces two break points at 15-40 when a positive backhand return draws a Konta error. Credit the Brit for going for a really brave second serve to save the first one, but she nets a backhand on the second and Halep has the break! The Romanian will now serve for the match...
Konta* 3-6, 4-4 Halep (*denotes next server) - Halep saves two break points and holds
Halep calls Darren Cahill onto the court, and the Aussie is very positive, telling his player how well she's competing and asking for one last push. Initially Halep did not seem very happy with Cahill, admonishing him for something or other - it was not clear what exactly. Shades of the Garbine Muguruza-Sam Sumyk set to on the weekend.
Konta then has a wonderful chance to force a break point at 30-30 but she sends an easy forehand long to make it 40-30. The Brit though earns a reprieve with a Halep error, and she does force a break point with a stunning drop shot-lob combo. Konta can't take it though, as she misses her return, and it's the same story a couple of points later as JoKo forces a second break point but sends her backhand return well wide. She really needs to start taking some of these opportunities. Halep then produces a big serve and a huge forehand winner up the line to fend off more danger and complete a vital hold.
Konta 3-6, 4-3 Halep* (*denotes next server)
Konta just being forced to go for more than she would like, and a pushed forehand goes long to make it 30-30. Big moments coming up, and JoKo steps up well and fires an ace out wide followed by a nerveless backhand volley to secure the hold and end the run of games against her.
Konta* 3-6, 3-3 Halep (*denotes next server)
Tennis really is a funny old sport, with sudden huge swings in momentum almost par for the course. Halep is now the far more aggressive player, and she ekes out a hold after giving up a 40-15 lead and being forced back to deuce.
The second set so far: Three games in a row for Konta; three in a row for Halep.
Konta 3-6, 3-2 Halep* (*denotes next server) - Halep breaks
Hmmm, those missed break points really could haunt JoKo, who is suddenly all over the shop and unable to keep the ball in play. Three mistakes gift Halep two break points, and she takes the second one with a sensational arcing forehand winner that skips away from Konta on the baseline. What a turnaround, that really came out of nowhere.
Konta* 3-6, 3-1 Halep (*denotes next server) - Halep saves two break points and holds
Halep is really struggling now, and she's spraying errors in the face of a barrage of Konta's heavy hitting. The Brit powers her way to 15-40 and two break points, but she squanders them both with a long forehand return and a ropey volley. Those were two big opportunities, and she makes two more errors to gift the game to Halep. Will that prove costly?
Konta 3-6, 3-0 Halep* (*denotes next server)
Konta starting to really impose herself now, and she holds to 15 to consolidate the break. Three games in a row, a huge shout of 'come on', and Konta is on a roll all of a sudden.
Konta* 3-6, 2-0 Halep (*denotes next server) - Konta breaks
This is some huge returning from Konta, and she forces three break points at 0-40 with a fizzing backhand return winner. Halep then nets a backhand limply, and Konta has broken to love!
What a perfect start to the second set for the British No 1.
Konta 3-6, 1-0 Halep* (*denotes next server)
No on-court coaching from either player at the end of the set, with Konta neglecting to call on Wim Fissette.
So important she holds here and gets on the front foot in the second set, but there are immediate danger signs as Halep flicks a forehand pass down the line to get into the game at 30-30. Konta though steps it up impressively on the next two points, and she seals the hold with a wonderful drive volley.
Konta* 3-6 Halep (*denotes next server) - Game and first set Halep
You'd expect some nerves from Halep here having just missed a couple of set points, but she keeps her cool and serves solidly to hold to love and seal the first set.
A very accomplished first set from the Romanian. Work to do for Konta, who's been a little loose with some of her groundstrokes.
Konta 3-5 Halep* (*denotes next server) - Konta saves two set points and holds
Konta serving to stay in the set, and she gets off to a good start with a forehand winner and unreturned serve to go up 30-0. Halep responds though by nailing a forehand winner, and when Konta nets a forehand it's 30-30 and the Romanian is just two points away from the first set. Make that one point - Konta double faults and it's 30-40, set point. It's very well saved by Konta, who plays the drop shot at just the right moment and gets her reward with an easy put-away volley. Halep though forces a second set point when Konta sends a backhand long, but again the Brit saves it - this time with a thunderous backhand winner crosscourt. Konta then reels of the next two points to complete the hold, sealing the game with another brilliant backhand winner. Things are starting to click for Jo on her favoured backhand wing.
Konta* 2-5 Halep (*denotes next server) - Halep saves a break point and holds
Amazing, Andy Murray-esque defence from Konta drives Halep to distraction and forces her to go for too much and spray a forehand well long to make it 30-30. Half a chance for Konta here, and it's deuce after Halep follows an ace with a forehand error. Another forehand error then makes it advantage Konta, and her first break point of the match. Can she take it? No, Halep saves it with an excellent inside-out forehand. The Romanian then draws a couple of errors from Konta on the next two points, and completes a very important service hold.
Konta 2-4 Halep* (*denotes next server)
For someone with such a diminutive frame, Halep can generate a huge amount of power from the baseline. Her forehand in particular has some real pop, and it helps her to 15-30 lead here against a pretty flustered looking Konta. The Brit responds with two huge first serves to go up 40-30, but Halep rips a backhand return winner down the line to lay down a real marker and force deuce. Konta does eventually hold though thanks to some more strong serving, and she ensures the deficit remains at just the one break of serve.
Konta* 1-4 Halep (*denotes next server)
These forehand to forehand exchanges are something to behold, and it's Konta who comes out on top in the latest one with a tremendous injection of pace to make it 30-15. Halep looks to be in control of the game when she takes the next point, but a couple of errors have us back at deuce. The Romanian does eventually hold though as Konta sprays a forehand and then a backhand wide.
Three games in a row for Halep.
Konta 1-3 Halep* (*denotes next server) - Halep breaks
An amazing stat from David Law in commentary is that no-one has won a higher percentage of points on their serve this year than Konta. She really has made such improvements over the last few months.
You just know that having said that, she will get broken this game...
Yep! A double fault makes it 15-15 to allow Halep into the game, and the Romanian unleashes on the forehand side to draw an error from Konta and make it 30-30. Halep is then similarly devastating on the next point to earn a 30-40 and the first break point of the match. And my word a second double fault of the game hands Halep the break!
Meanwhile, here's that Halep flakiness I was talking about:
Halep leads 3-1 over Konta but only just favourite with the bookies...... Interesting— Chris Goldsmith (@TheTennisTalker) March 29, 2017
Konta* 1-2 Halep (*denotes next server)
Konta gets a good look at a few forehands, but she's a little wayward and allows Halep to hold to 15 having led 0-15. Not a lot to choose between the players so far.
Johanna Konta bidding to become the first British woman to reach the semi-finals in Miami as she takes on Simona Halep. pic.twitter.com/z6uMYwOBtb— Stuart Fraser (@stu_fraser) March 29, 2017
Konta 1-1 Halep* (*denotes next server)
The Konta service machine looks to be in good working order, and she holds to love thanks to some very steady serving and big hitting on the forehand side.
Konta* 0-1 Halep (*denotes next server)
Strong serving from Halep takes her to 40-0, but Konta rips a backhand return winner to reduce the deficit to 40-15. The Brit then sends a forehand long however, and it's a comfortable Halep hold to kick things off.
The players have completed their warm-up, and we're under way, Halep serving first.
It's a beautiful afternoon in Miami, with temperatures at about 28 degrees.
Just a note on that Wuhan match when these two last met, Konta was 5-1 down in the final set before reeling off six straight games to nick it 7-5.
Halep is known for being frail sometimes mentally, and that collapse could be playing on her mind tonight.
Evening all, welcome to our live coverage of the Miami Open quarter-final between Britain's Johanna Konta and the world No 5 Simona Halep.
These two have met just once before, with Konta winning 7-5 in the third set in Wuhan two years ago, so we should be in for a tight affair this afternoon.
This time a year ago Konta created a big stir when she became the first British woman ever to reach the last eight of a WTA Premier mandatory tournament, but nowadays we just expect this sort of thing from her. She really has been remarkably consistent, and now the challenge is turning the frequent quarter-final and semi-final appearances into more regular tournament wins. For a world No 11, Konta's two WTA titles is a little under what you would expect.
Her opponent today will offer a very stern examination. Halep is arguably the strongest player on the tour not to have won a major, and she is getting back to full strength with coach Darren Cahill after suffering a rotten run of injuries.
Prone to the odd mental lapse, she showed great mental strength in her fourth round encounter with Sam Stosur on Monday to save a match point and eventually prevail in three sets.
And that's the scoreline I'm predicting today - Halep to come through in three.
Konta v Halep
Johanna Konta and Simona Halep will be on court at about 6pm BST for their Miami Open semi-final, and we'll bringing you game by game updates as the Brit looks to reach the last four.
Prior to the match starting, have a read of our preview below. Konta remember reached this stage last year but was beaten in straight sets by eventual champion Victoria Azarenka.
Konta knows she has a tough task in front of her as she aims to make the Miami Open semi-finals.
The British number one matched her 2016 run to the quarter-finals by beating Spaniard Lara Arruabarrena 7-5 6-1 in a tricky fourth-round contest in Florida.
That set up a last-eight meeting with third seed Simona Halep, who saved a match point to beat Sam Stosur in three sets.
Although the Romanian has struggled with injury and form so far in 2017, Konta, typically, is not looking too far ahead.
"I'm happy that I'm still here and get to play another match," she said in her post-match press conference before she found out the identity of her opponent. "I don't necessary believe in open fields because every single player in this draw is world class. So every match is as tough as the next.
"I'm just happy to be still part of the event, and whoever I play next I know it'll be a tough game and I look forward to being a part of it."
A much more difficult night looked on the cards for the 10th seed as Arruabarrena, who had only won one match this year prior to arriving in Miami, played superbly in the opening set and only some impressive serving from Konta kept her in it.
And at 6-5 she raised her return game as well, breaking Arruabarrena to take the opener. She timed it nicely as it was the first time she had been ahead in a service game of the Spaniard's.
The second set was a different story, as Konta began to flex her muscles and hit her opponent off the court on her way to a 4-0 lead.
A slight mishap saw Arruabarrena break to avoid a bagel, but Konta shut down any hopes of a comeback by seeing out the second set and the match.
On her performance, Konta added: "I felt I played myself more into the match a bit more. As the match went on, I felt clearer and clearer on how I wanted to play and what I wanted to do out there from my perspective.
"I'm quite happy I was able to execute that reasonably well. And also make it tough for her to stay in that match with the level that she was playing at."