"So now, if anything, it should motivate me more. I know she's a fighter and she's really strong. She's great. I think she's really happy now that she knows what it is after all this time."
Serena now awaits the winner of Victoria Azarenka of Belarus, the No. 4 seed in this year's draw, and Gisela Dulko of Argentina.
Two former No. 1s and a past French Open champion all advanced to the third round of the U.S. Open early Thursday afternoon.
Former world No. 1 Ana Ivanovic faced even less of a test, advancing with a walkover against Petra Cetkovsa because of a left thigh injury. Cetkvosa had beaten Ivanovic in the third round of Wimbledon.
"I felt good and I was excited for today's match and opportunity for revenge," the Serbian said. "But just have to keep that momentum. Now I get an extra day off, which is always nice."
Ivanovic, who has struggled to regain her form since reaching No. 1 in 2008, reached the fourth round last year at Flushing Meadows. The No. 16 seed will try to get back there when she faces Sloane Stephens.
Another former No. 1, Jelena Jankovic, took out Jelena Dokic 6-4, 6-4. The 11th-seeded Serbian, who is rumored to be feuding with Maria Sharapova, now takes on the 17th seed Anastasia Pavlyuchenkova, who powered off Petra Martic of Croatia, 6-4, 2-6, 6-4.
Other seeds advanced were 10th seeded Andrea Petkovic of Germany, who beat China's Zheng Jie 3-6, 6-3, 6-3; 15th seeded Svetlana Kuznetsova, who
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