Stosur defeated Misaki Doi 6-2, 6-4 with five breaks in nine receiving games. Stosur had her serve broken once in each set but still won two-thirds of the points on serve.
Marion Bartoli, the second seed, rolled to a 6-1, 6-2 win over Vania King in her second-round match. Bartoli saved all three of the break points she faced, losing just 13 points over eight service games.
No. 6-seeded Ayumi Morita, the only Japanese player left in the field, moved into the quarterfinals with a 6-2, 6-3 win over Eleni Daniilidou by fighting off nine of Daniilidou's 11 break-point chances.
Thursday's fourth match saw seventh-seeded Chanelle Scheepers get by Yaroslava Shvedova 4-6, 6-3, 7-6 (7-5).
Stosur draws Scheepers and fourth-seeded Petra Cetkovska goes against Zheng Jie in Friday's quarterfinals in the top of the bracket. Bartoli faces Morita and No. 3- seeded Angelique Kerber plays defending champion Tamarine Tanasugarn in the other half of the draw.