The top-seeded Azarenka, the defending Australian Open champion, needed an hour to dispatch the 25th-seeded Kuznetsova 6-1, 6-2 and advance to a meeting against 14th seed Julia Goerges.
Azarenka won 83 percent of her first-serve points and had serve broken just once. Her win came two days after she was nearly upset in the first round by Germany's Mona Barthel.
Also advancing was Li Na of China, who topped countrywoman Zheng Jie 6-1, 6-3. It was Li's first win over Zheng in four meetings and the first time the two had met in six years.
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