The 27-year-old, a close friend of fellow Belgian and former Grand Slam champion Kim Clijsters, wore down the more powerful Kvitova in two hours and five minutes of attritional tennis under the Centre Court roof.
Czech eighth seed Kvitova, who beat Maria Sharapova in the 2011 Wimbledon final, paid the price for an erratic display and Flipkens took full advantage to reach her first Grand Slam semi-final, against 2007 runner-up Marion Bartoli of France on Thursday.
Flipkens is the first Belgian to make the last four at Wimbledon since Justine Henin in 2007, an achievement she would have found impossible to imagine just 12 months ago.
This time last year the 2003 junior Wimbledon champion was ranked a lowly 262nd in the world after blood clots in her left ankle forced her to take several months off, but she has recovered from that setback in remarkable fashion.
“It’s amazing, it’s more than a dream come true to be in the semi-final of a Grand Slam, it’s ridiculous,” Flipkens said.
“Last year I didn’t even get into the qualifying of Wimbledon.
“I still cannot believe it. I was so calm on the court, I had nothing to lose and I just went for my shots.
“Kim (Clijsters) was one of the few people last year really believing in me.
“I am so happy you cannot imagine. I don’t even have tears.”
The diminutive 27-year-old, who had failed to get past the third round in five previous Wimbledon appearances, hadn’t dropped a set en route to the last eight and she never looked intimidated by Kvitova’s hard-hitting style.
Kvitova landed the first break for a 3-2 lead and recovered from dropping her serve in the next game to break again to move 4-3 ahead.
Given the chance to serve out the set, Kvitova seemed wracked with nerves and had to save four break points before finally converting her third set point.
But Flipkens, a striking figure in her tinted prescription sunglasses and white bandana, responded superbly.
The Belgian cleverly moved Kvitova out of position with her accurate ground-strokes and broke in the sixth game to take the second set.
Kvitova had her temperature taken by a doctor after calling for treatment at 5-2 in that second set and she couldn’t turn the tide of a match rapidly getting away from her.
Flipkens broke for a 5-4 lead in the decider when the Czech missed an easy forehand.
And she finished the job with an ace on her third match point before slumping to the turf in delight.