Sharapova -- the event's second seed, and this year's U.S. Open champion -- topped sixth-seeded Belgian Kim Clijsters, 6-4, 6-4. Kuznetsova, the French Open runner-up, beat seventh-seeded fellow Russian Elena Dementieva (0-2), 7-5, 6-3. No. 8 Hingis beat fifth-seeded Nadia Petrova, 6-4, 3-6, 6-3.
Sharapova broke Clijsters' serve three times and had 11 more winners (24-13).
Hingis broke Petrova's serve five times. Petrova, who knocked off world No. 1 Amelie Mauresmo, had seven double faults against Hingis.
The tournament includes the top-eight women in the world, divided into two groups.
Mauresmo (0-1), Justine Henin-Hardenne (0-1), Petrova (1-1) and Hingis (1-0) make up the "Yellow Group." The "Red Group" consists of Sharapova, Kuznetsova, Clijsters and Dementieva.