Two days after conquering 2011 Paris winner Li Na, doubles specialist Shvedova looked set to become the first player from her nation, and the first qualifier, to reach the semi-finals here as she led Kvitova 4-2 in the final set.
But the Czech hauled herself back before finally ending the adventure of 142nd-ranked Kazakh qualifier Shvedova, keeping her focus through driving rain to complete victory after her 142nd-ranked opponent drilled a backhand wide on matchpoint, and setting up a meeting with the woman she beat in last year's Wimbledon final.
"I expected it will be tough match and it was actually," Kvitova said.
"She start well and I was very nervous from the beginning. The first set I did easy mistakes. Then I knew that I had to change my game and I have to be the aggressive one and going for the points. The games were very close. I'm happy that I won the big points. I couldn't give up."
The bespectacled Shvedova had shown no fear or nerves in spinning holder Li Na out of the tournament in the previous round and she also left Kvitova in a daze.
The Kazakh stood two games away from booting out yet another grand-slam winner from a topsy-turvy French Open, where only three women lived up to their seedings in reaching the last eight, but in the end Kvitova relied on her ice-cool temperament to dig herself out of a hole.
Such was her focus that she did not even blink when she started to get drenched in the driving rain sweeping through the court and levelled for 4-4 as a rapidly tiring Shvedova was briefly forced to toss aside her blue-framed prescription glasses.
Kvitova, though, made the most of her 20/20 vision to earn her first match point but let out a piercing squeal as she hit a wild forehand long and wide. She made no mistake on the second as Shvedova smacked a backhand wide to bow out.
"I was just super-tired. I had zero energy left," Shvedova said after losing out on her chance to become the first qualifier and first player from her nation to reach the women's semis in Paris.
Kvitova will next take on title favourite Maria Sharapova for a place in Saturday's final, and does so after winning five consecutive matches for the first time since January.
"It's good to know that I can play and I hope that it will be not only five," she said.
"But I know Maria is a tough opponent. I lost in the [last two] matches [against her]. She's playing very well. She has a great season right now, and she's very tough opponent."