Stosur is ranked 17th in the world, but this was the third win in four tries for Stosur against the fourth-ranked Radwanska. They had not faced each other in two years.
After outlasting Radwanska 7-5, 2-6, 6-3, Stosur will face Virginie Razzano in the semifinals. Razzano pulled off another upset when she dispatched third-seeded Petra Kvitova 6-7 (6-8), 7-5, 7-6 (10-8) in a match that lasted 3 hours, 35 minutes.
Ivanovic survived against fourth-seeded Roberta Vinci 6-1, 6-7 (1-7), 6-2 and Azarenka took out Urszula Radwanska 6-1, 6-2.
This was the second straight tournament in which both Radwanska sisters reached the quarterfinals.