Zvonareva, a bronze medalist at last month's Olympics, will next face Italy's Karin Knapp, who beat eighth-seeded Mariya Koryttseva of Ukraine on Wednesday.
Austria's Tamira Paszek defeated seventh-seeded Pauline Parmentier of France 6-2, 2-6, 6-3, setting up a clash with China's Zheng Jie, who beat Romania's Raluca Ioana Olaru 6-4, 6-0.
Fourth-seeded Peng Shuai of China also progressed, downing compatriot Lu Jingjing 6-3, 6-4. She will face unseeded American veteran Jill Craybas, who on Wednesday upset sixth-seeded Olga Govortsova of Belarus.
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