The 37-year-old American improved to 7-3 on the season as she clinched the victory on the second match point when the 21-year-old Russian smacked a forehand wide.
Williams trailed 2-5 in the first set but won five straight games to take the opener. She also rallied in the second set, falling behind 0-3 before winning six of the next seven for the victory.
Williams advances to the third round where she will face 29th seeded Kiki Bertens of the Netherlands, who outlasted American Varvara Lepchenko 5-7, 7-6 (7/5), 6-1.
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