In the men's quarterfinals, top-seeded Richard Gasquet ousted Russian wild-card entry Teimuraz Gabashvili 6-3, 6-2, and defending champion Andreas Seppi of Italy made it to his fifth semifinal of the season after Edouard Roger-Vasselin retired because of a strained neck while trailing 5-2.
Stosur-Ivanovic was a rematch of last year's three-set semifinal match between former Grand Slam champions. Ivanovic took a 3-0 lead but Stosur broke back twice to win the opening set. An early break in the second was enough for the Australian to defeat the former top-ranked Ivanovic for the second straight year.
"I certainly had a few things in my head that I wanted to try to do today against her," Stosur said. "And right from the start it was kind of working and from that my confidence kind of built, and I was able to keep going and play well till the end."
Last Sunday, Stosur won the fifth title of her career in Osaka, Japan, while Ivanovic lost in the final in Linz. Austria.
Kuznetsova, a two-time Grand Slam champion, broke twice in the first set. But Vinci offered more resistance in the second, trading breaks twice before the Russian took a 4-2 lead.
"Today I played really well in the first set with some slight mistakes in the second, which I managed to overcome," Kuznetsova said.
The Russian will be playing in her first semifinal this season and her first at a home event since she lost to Serena Williams in 2007.
Gasquet broke early in the first set and took a 4-0 lead in the second to eliminate the last Russian left in the draw. The Frenchman is looking for the eighth spot at the ATP finals in London next month. But he made an early exit at Shanghai last week and dropped to 10th in the rankings, hurting his chances of qualifying.
Gasquet will next play Croatian veteran Ivo Karlovic, who advanced to his second semifinal of the season by winning eight consecutive games and serving 11 aces to rout Russian teenager Karen Khachanov 6-4, 6-0.
Roger-Vasselin strained his neck during the warmup and received treatment after the first game.
"From his first service game and down in the match he couldn't serve normally," Seppi said. "I would never like to win like this, but sometimes it happens."