Kuznetsova, a two-time Grand Slam winner, hit seven aces in the match and will next face 15th-seeded Sorana Cirstea of Romania. Cirstea beat Japanese wild card Misaki Doi 6-1, 6-2.
In other second-round matches, Eugenie Bouchard of Canada outlasted ninth-seeded Sloane Stephens of the United States 5-7, 7-6 (7), 6-3; No. 11-seeded Ana Ivanovic of Serbia beat Elina Svitolina of Ukraine 6-3, 6-0; and 16th-seeded Dominika Cibulkova of Slovakia defeated Casey Dellacqua of Australia 7-5, 6-3.
Serena Williams pulled out of the $2.3 million tournament to recover from a busy summer schedule.