Melbourne, Australia (SportsNetwork.com) - World No. 1 Serena Williams had to shake off a slow start before dispatching Vera Zvonareva in Thursday's second round of the Australian Open.

Williams trailed late in the first set before ultimately taking a 7-5, 6-0 win over the unseeded Zvonareva of Russia.

It was a rematch of the 2010 Wimbledon final between the two, a match that Williams won 6-3, 6-2.

Fourth-seeded Petra Kvitova, the reigning Wimbledon champion and last week's Sydney titlist, took care of German Mona Barthel 6-2, 6-4. Meanwhile, sixth- seeded Agnieszka Radwanska dispatched Johanna Larsson 6-0, 6-1 to also move on in Melbourne.

Serena's sister, Venus, who was a finalist at the 2003 Aussie Open, had a much easier time defeating fellow American Lauren Davis 6-2, 6-3.

Tournament officials confirmed on Wednesday that the Williams sisters pulled out of their doubles draw, but they did not specify a reason.

Slovak and 11th-seeded Dominika Cibulkova downed Tsvetana Pironkova of Bulgaria 6-2, 6-0.

American Madison Keys pulled a minor upset of 29th-seeded Casey Dellacqua with a 2-6, 6-1, 6-1 win.

In other action, 19th-seeded Alize Cornet defeated Denisa Allertova 6-4, 6-7 (2-7), 6-2; 24th-seeded Garbine Muguruza dropped Daniela Hantuchova 6-1, 1-6, 6-0; 25th-seeded Barbora Zahlavova Strycova moved past Kai-Chen Chang 6-1, 7-5; No. 26 seed Elina Svitolina worked past Nicole Gibbs 7-6 (7-3), 7-6 (8-6); 30th-seeded Varvara Lepchenko defeated Ajla Tomljanovic 6-1, 7-6 (7-1); Swiss Timea Bacsinszky beat Anna Tatishvili 6-7 (5-7), 6-3, 6-2; Italian Camila Giorgi eased past Tereza Smitkova 6-1, 6-4; and American Madison Brengle cruised past compatriot 6-1, 6-3.