Her next opponent is Australia's Casey Dellacqua, who beat Serbia's Bojana Jovanovski 6-3 6-2.
CNN: No. 1 Wozniacki wins Melbourne opener
Kvitova's teammates Andrea Hlavackova and Lucie Hradecka then beat Ashleigh Barty and Casey Dellacqua 6-0 7-6 (7-1).
CNN: Nadal poised for Chile comeback double
It was the second left-hander Williams has played and she will meet another in the last 32 after unseeded Australian Casey Dellacqua defeated Karolina Sprem 7-6 7-6.
CNN: Williams pair continue smooth progress
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