Kuznetsova, 2004 champion and fourth-seeded this year, defeated Czech Klara Zakopalova 6-2, 6-3. The two-time major finalist was last year's runner-up at the French Open.
Hingis swept past France's Mathilde Johansson 6-0, 6-3. The former world No. 1 and five-time major title winner, Hingis was the U.S. Open champ in 1997 and the back-to-back runner-up in 1998 and 1999.
Vaidisova is playing her first tennis since early July after being sidelined with a mono-like illness.
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