A finalist last year and one of the favourites to win the title this season, the Belarussian overcame a shaky start to beat Alize Cornet of France 6-7(2) 6-3 6-2.
Azarenka's next opponent is former world number Ana Ivanovic, who also came from behind to win her center court clash with American Christina Mchale 4-6 7-5 6-4.
"In the first set, Alize played really well and I made too many mistakes," Azarenka said.
"I wasn't patient enough. I had a lot of chances and I didn't convert them.
"The difference in the second and third sets was I played a bit more aggressive and when I got my chances I did convert them."
(Reporting by Julian Linden; Editing by Gene Cherry)
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