Wozniacki, the current world No. 1, edged past Dominika Cibulkova 7-5, 2-6, 6-4 by winning the final six games of the second-round match. Wozniacki dropped serve six times and needed three breaks in the final set to survive.
Kvitova, No. 2 in the rankings but who could overtake Wozniacki with a championship in Sydney, just got by Alexandra Dulgheru 5-7, 6-3, 6-4. Kvitova fought off nine of the 12 break points she faced and won just one more point (96-95) than Dulgheru in the win.
Third-seeded Victoria Azarenka had an easier time in her second-round match, topping Jelena Jankovic 6-4, 6-2, and fourth-seeded Li Na, the tournament defending champion, was pushed to a third set for a 2-6, 6-4, 6-1 win over Chanelle Scheepers.
No. 7-seeded Agnieszka Radwanska defeated Andrea Petkovic 7-5, 6-4 and eighth-seeded Marion Bartoli sailed past Jelena Dokic 6-0, 6-3.
Daniela Hantuchova beat Francesca Schiavone 7-5, 6-1 and Lucie Safarova, who was ahead 6-1, 2-0 when Svetlana Kuznetsova retired, also advanced.
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