Azarenka, despite five double faults, defeated Sabine Lisicki 6-4, 6-2. Azarenka had five breaks in nine receiving games, easily offsetting the two breaks she suffered.
Defending champion and world No. 3 Agnieszka Radwanska had little trouble in a 6-2, 6-3 decision over Zhang Shuai. Radwanska did lose her serve once in the second set but that was the only break-point chance she allowed Zhang.
Julia Goerges outlasted eighth-seeded Samantha Stosur 7-6 (7-2), 4-6, 7-5, saving 10 break points in the process. She finished off three of her six break opportunities, including both in the third set.
Also, ninth-seeded Marion Bartoli beat Ayumi Morita 6-4, 6-3 and 10th-seeded Caroline Wozniacki controlled the third set in a 6-7 (5-7), 7-6 (7-3), 6-0 win over Hsieh Su-Wei.
Other second-round winners Tuesday were Romina Oprandi, Jelena Jankovic and Lourdes Dominguez-Lino.