All 32 seeded players in the tournament received a bye past the first round and Williams opened her bid for a fourth title by defeating Sorana Cirstea 6-4, 6-3. Kuznetsova, the reigning French Open champion, was a 6-2, 3-6, 6-4 winner over Peng Shuai.
Of the 16 seeds in action Thursday, six were eliminated.
The highest-seeded player to fall was No. 8 Li Na, who lost to Timea Bacsinszky 6-4, 4-6, 7-6 (7-3). No. 10 Flavia Pennetta lost to Andrea Petkovic 6-3, 3-6, 6-0.
In the third round, Kuznetsova will face 27th-seeded Agnes Szavay and Williams will play unseeded Roberta Vinci.
Sixth-seeded Agnieszka Radwanska advanced with a 7-5, 6-0 victory over Ekaterina Makarova.
Yanina Wickmayer, the 12th seed, defeated Elena Baltacha 6-1, 6-3 and No. 13 Marion Bartoli ousted Magdalena Rybarikova 6-2, 6-4.
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