Azarenka piled up six breaks in a 6-3, 6-3 victory over Sabine Lisicki. Azarenka had three breaks in each set that allowed her to offset three dropped service games on the day.
She won a relatively low 53 percent of the points on serve but took 54 percent of the points off Lisicki's serve.
Fourth-seeded Angelique Kerber barely survived a 2 1/2-hour challenge from Monica Puig, winning 3-6, 6-4, 7-6 (9-7). Kerber lost her serve seven times but only once in the third set in forcing the final tiebreaker.
Also Wednesday in the second round Sloane Stephens stopped Sofia Arvidsson 6-3, 6-4 and Lesia Tsurenko, inserted in to the draw when world No. 2 Maria Sharapova withdrew due to a shoulder injury, beat Jarmila Gajdosova 1-6, 6-1, 6-4.
Stephens moves into a quarterfinal match against third-seeded Serena Williams, who is along with Azarenka and Kerber, one of three seeded players left in the tournament.