American veteran Madison Keys stopped the Iga Swiatek train in spectacular style, coming from behind to edge a three-set epic by the smallest margin possible.

Swiatek had been untouchable at the Australian Open to date, dropping only 14 games across the first five rounds. But the players she had beaten – who included Emma Navarro and Emma Raducanu – were all line-and-length types with medium-paced shots and scampering movement.

Keys is the opposite: perhaps the heaviest hitter on the women’s tour, with the possible exception of the woman she will now face in the final, Aryna Sabalenka.

Keys’s serve, in particular, is an absolute blunderbuss, reaching a maximum figure – 120mph – that would not look out of place in the men’s draw. And it was to that serve that she turned at 7-8 down in the deciding-set tie-break.

Crunch: an ace out wide to level the scores. Boom: another serve on to the sideline, which Swiatek parried but could not direct back into court. Keys had match-point for a place in her first major final in eight years. A few seconds later, Swiatek had fired one final forehand long, and Keys was through, by a 5-7, 6-1, 7-6 scoreline.

This has been a tale of perseverance. While Keys is only 29, she has been playing at these events since she was 16, and has often been tipped as a major champion of the future. The nearest she came was the US Open final of 2017, where she was thumped by her close friend Sloane Stephens, winning only three games. This time, she is more mature, and will surely put up more resistance.

“During that match [the 2017 US Open final], I was so consumed with being nervous and the moment and the opportunity and all of that, that I never really gave myself a chance to actually play,” Keys said.

“The big thing for me has just been knowing that there are going to be a lot of moments where I’m uncomfortable in the match. It’s going to be stressful. You have thousands of people watching you. You might not be playing your best tennis.

“But instead of trying to shy away from that and search for settling or comfort or anything, just being OK that that’s the situation, and you can also play tennis through that, I think is something that I’ve been working really hard on.”

As it happens, Rod Laver Arena had hosted another match between a pair of self-styled “soulmates” in the earlier part of Thursday evening. This one pitted Sabalenka – world No 1 and defending champion – against Paula Badosa of Spain. And it was one-sided, with Sabalenka closing out a 6-4, 6-2 victory in a little under an hour and a half.

It briefly looked as if another upset could be on the cards when Badosa got off to a misleadingly fast start by winning the opening two games. At that stage, Sabalenka was firing unforced errors in all directions: six of them in the first 13 points. She seemed confounded by her own frightening power off the ground, as if trying to ride a high-speed motorbike for the first time. But she gradually found her balance and then the engine started purring.

From 0-2 down, Sabalenka won 12 of the next 16 games to surge home. Her statistics in that dominant period showed 31 clean winners and just 15 more unforced errors: a two-to-one ratio which is rare in either draw, but particularly so on the women’s side. Towards the end of the match, Badosa found herself so far off the pace that she celebrated a rare hold of serve by thrusting both arms in the air.

“Everything she was touching today could become gold,” said Badosa afterwards. “I feel like she’s playing a PlayStation. If she plays like this, I mean, we can already give her the trophy.”