Azarenka posted a 6-4, 6-2 win over Roberta Vinci. She broke open a tight match, which was tied 4-4 in the first set, by winning six consecutive games. That gave her the first set and a 4-0 lead in the second.
Vinci had her chances in the match but Azarenka held off 8-of-10 break points she saw while cashing in 5-of-9 against Vinci.
Azarenka next goes against fifth-seeded Angelique Kerber, who routed Urszula Radwanska 6-1, 6-1 in 47 minutes. Kerber won 79 percent of the points on serve and 61 percent off Radwanska's serve.
No. 3-seeded and defending champion Agnieszka Radwanska, the sister of Urszula Radwanska, defeated Jamie Hampton 6-4, 6-3 by piling up five breaks. She'll meet 10th-seeded Caroline Wozniacki, who pulled off a small upset in a 4-6, 6-3, 6-4 victory over No. 7-seeded Li Na, in the third round.
No. 2-seeded Maria Sharapova posted a 6-2, 7-6 (7-5) win over 16th-seeded Lucie Safarova, setting up a third-round match against eighth-seeded Samantha Stosur. Stosur got by No. 12 Dominika Cibulkova 6-4, 7-5.
Also Wednesday, sixth-seeded Sara Errani rallied for a 3-6, 6-2, 6-2 win over ninth-seed Marion Bartoli and 17th-seeded Nadia Petrova edged Petra Martic 7-6 (7-2), 6-7 (1-7), 6-4 in a 3-hour, 10-minute marathon.