Williams claimed a 6-0, 6-1 win over Anna Chakvetadze in just 49 minutes. Williams, the tournament's defending champion, won the first 11 games before Chakvetadze was able to avoid the shutout.
Williams won 68 percent of the points in the match and took more points on Chakvetadze's serve (23-13) than Chakvetadze.
Third-seeded Caroline Wozniacki also breezed into the third round, dropping Kai-Chen Chang 6-4, 6-3 behind an effort that had only 11 unforced errors.
Seventh-seeded Agnieszka Radwanska roared by Alberta Brianti 6-2, 6-0 and No.
9-seeded Na Li stopped Kurumi Nara 6-2, 6-4 in just more than an hour while 10th-seeded Flavia Pennetta ripped Monica Niculescu 6-1, 6-1.
No. 14-seeded Victoria Azarenka, who beat Bojana Jovanovski, and 16th-seeded Maria Sharapova, who dispatched Ioana Raluca Olaru, both won by scores of 6-1, 6-4.
Klara Zakopalova defeated No. 18-seeded Aravane Rezai 5-7, 6-3, 6-3; Anastasia Rodionova ousted 19th-seeded Svetlana Kuznetsova 6-4, 2-6, 6-4; and Petra Kvitova took out 23rd-seeded Jie Zheng 6-4, 2-6, 6-2 in the day's upsets.
Other seeded players moving into the third round were No. 29 Anastasia
Pavlyuchenkova, 31st-seeded Alexandra Dulgheru and No. 32 Sara Errani.
Unseeded winners Thursday were Barbora Zahlavova Strycova, Kaia Kanepi and Dominika Cibulkova.
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