Kvitova, the last champion left in the draw, took the first 6-4, but the Belgian kept her cool to take the next two sets 6-3 6-4 under the Centre Court roof.
She will meet 15th seed Marion Bartoli in the semi-finals after the Frenchwoman overcame talented American Sloane Stephens 6-4 7-5.
Bartoli beat Stephens in a bizarre rain-interrupted quarter-final that featured eight successive breaks of serve on Tuesday to leave the French 15th seed one match away from a surprise second Wimbledon final.
Bartoli, beaten by Venus Williams in the 2007 final, snaffled the first set by winning the first two points played after a two and a half hour rain break.
There followed an extraordinary second set that included eight straight dropped service games as Stephens, the only remaining American in the either singles competition, garnered only one point in four service games.
Both women finally managed a hold each before Bartoli, yet to drop a set in five matches in the tournament, broke to love to secure a semi-final clash with Belgian Kirsten Flipkens who upset 2011 champion Petra Kvitova.
"I've felt great here since 2007, obviously grass suits me," said Bartoli who was not so enamoured with the lush lawns when refusing to play on in light drizzle late in the first set.
"The courts are already a bit slippery anyway and they can get dangerous when it gets wet so I don't know why the crowd got against me for that," she said after being booed for making her stand while Stephens was keen to play on.
"I was returning extremely well but not serving well - the opposite of before the rain delay really. I just need to put the two together in the next match."
Having been denied their expected roll call of star names by last week's upsets, the crowd took a while to comprehend what was different about Tuesday's match but gradually realised that it was the peace and quiet.
After years of suffering the screeching and grunting that has pervaded the top end of the women's game, Number One court was an oasis of calm.
Bartoli is always a blur of movement, leaping and fidgeting like a toddler at the table, but she does go through her manic routine quietly.
Stephens is off the scale, seemingly without emotion at any stage of a contest that turned into "Sloane motion" v perpetual motion.
Even during the drizzle debate, Stephens stood phlegmatically at the base line playing no part in the discussions as the crowed slow-clapped and hooted.
The match went with serve until the covers came on at 5-4 to Bartoli, deuce on the Stephens serve.
When play resumed the Frenchwoman took the first two points, the decider courtesy of a shocking netted forehand by Stephens, to seal the set.
The 20-year-old American had emerged from the rain break dressed for an Arctic expedition and played as if she would rather have been back in a warm changing room as Bartoli took the first two games of the second set to love.
The second was the first of a crazy run of eight breaks in a row, most of the points handed over by errors.
Stephens, who reached the Australian Open semi-finals in January, eventually started to land her free-swinging ground shots but she lacked control and was unable to stay in any rally long enough to lever a regular advantage.
Bartoli's punchy double-handers were similarly inconsistent before both players did manage to hold serve.
Stevens needed one more hold to force a tiebreak but she produced another horror show, broken to love as Bartoli strode into the most unlikely of semi-finals with a growing belief that this could be her year.
Kvitova joined the likes of Serena Williams, Maria Sharapova, Victoria Azarenka and Li Na on the All England Club scrapheap after being suffocated under Centre Court's closed roof.
All seemed on track when eighth seed Kvitova took the first set but she came unstuck in the second and called on the trainer after falling behind 5-2.
She popped a pill and had her temperature checked and although she appeared to get a second wind after surrendering the second set, a rush of blood when she charged to the net and fired a forehand volley long at break point down in the ninth game cost her dear.
Bespectacled Belgian outsider Flipkens, who is known as Flipper on the tour, kept her cool to serve out a momentous victory with an ace.
It's amazing, it's more than a dream come true. To be in the semi-finals of a grand slam is ridiculous," a wide-eyed Flipkens, nicknamed Flipper, said as she tried to digest her success.
"I still can't believe it"
One person who did believe in her was her friend and training partner Kim Clijsters.
"Still drying my eyes :-)) So proud of how @FlipperKF handled the big occasion for the first time," the former world number one tweeted even before Flipkens had walked off court.
Kvitova had been installed as a title favourite after all the pre-tournament front-runners fell by the wayside but she paid the price for a rush of blood in the ninth game of the third set when she charged to the net and fired a forehand volley long at break point down.
The Czech eighth seed, who gulped down a tablet and had her temperature checked when trailing 5-2 in the second set, was left to swallow a bitter pill as she watched Flipkens fire an ace on match point to seal her fate.
A stony-faced Kvitova was not convinced that it had been a winning shot, challenging Hawk-eye to overturn the call.
To all those watching on Centre Court, it only delayed the inevitable as the puff of white chalk dust had confirmed Kvitova's demise.
As Flipkins looked forward to her semi-final against 2007 runner-up Marion Bartoli, there was only one person she wanted to thank.
"Kim (Clijsters) was one of the few people last year still believing in me, I really have to thank her. People who were believing me I could count on one hand, but I'm just enjoying every moment now."
- Sports & Recreation
- Marion Bartoli
- Sloane Stephens
- Petra Kvitova