Kvitova staggered in the second set before taking a 6-2, 2-6, 6-4 decision over Carla Suarez Navarro. Kvitova had 48 unforced errors and lost three of the four break points she faced.
After the second set in which she had 17 unforced errors, Kvitova was able to convert a pair of third-set breaks and advance to the third round.
Sharapova, seeded fourth, won nearly two-thirds of the points in a 6-0, 6-1 romp over Jamie Hampton. Sharapova won 72 percent of the points on serve, including all three of Hampton's break-point chances. Sharapova has lost two games over her first two matches in Melbourne.
The No. 12-seeded Williams used a 22-minute first set en route to a 6-0, 6-4 win over Barbora Zahlavova Strycova. Williams lost just nine points in the first set.
No. 7-seeded Vera Zvonareva defeated Lucie Hradecka 6-1, 7-6 (7-3) and ninth-seeded Marion Bartoli stopped Jelena Dokic 6-3, 6-2 while No. 14-seeded Sabine Lisicki was a 6-1, 6-2 winner over Shahar Peer.
Sorana Cirstea got past Urszula Radwanska 1-6, 6-2, 6-3 in a match between unseeded players.