Virginie Razzano stuns Petra Kvitova
Razzano, the Italian ranked No. 131 in the world, squandered four match points and had to stave off two match points from Kvitova in the third-set tiebreaker before Kvitova double-faulted to end the match at 3 hours, 35 minutes.
"I think I was nervous," Razzano said. "I'm human. I'm not a robot. Sometimes you feel stress. I tried to focus on the points."
Razzano will face fifth-seeded Sam Stosur of Australia, a 7-5, 2-6, 6-3 winner over second-seeded Agnieszka Radwanska of Poland.
In the other quarterfinals, top-seeded Victoria Azarenka of Belarus routed Poland's Urszula Radwanska 6-1, 6-2, and seventh-seeded Ana Ivanovic of Serbia beat fourth-seeded Roberta Vinci of Italy 6-1, 6-7 (1), 6-2.
Hingis, the former top-ranked Swiss star, was playing her first WTA event in nearly six years.
Razzano's win over the seventh-ranked Kvitova was the Italian's first over a top-10 player since she handed then-No. 5 Serena Williams her first opening-round loss in Grand Slam event at the 2012 French Open.
After winning a tight second set, Razzano was serving at 5-3 in the third set when she wasted three match points on two hitting errors and a double fault.
"In my head, I never lost," Razzano said. "I stayed positive and never thought I could lose."
In the third-set tiebreaker, Kvitova jumped out in front 5-2 before Razzano battled back to even the score. Razzano saved one match point when Kvitova committed an unforced error, then dropped her fourth match point at 7-6. After another unforced error by Kvitova on the Czech's second match point, Razzano hit a forehand winner to set up match point No. 5, which ended with Kvitova's eighth double fault.