The third-seeded Kvitova, who downed current world No. 1 Victoria Azarenka in last year's Madrid finale, breezed past New Zealand's Marina Erakovic 6-2, 6-3 Monday. She advances to face fellow Czech Lucie Hradecka.
The ninth-seeded American Williams pasted Russian Elena Vesnina 6-3, 6-1, firing 14 aces and not allowing a single break point chance to her opponent in the triumph. Williams next will take on Russian Anastasia Pavlyuchenkova.
Serena's sister Venus dropped a second-round decision to 12th-seeded German Angelique Kerber 6-4, 6-1.
Fifth-seeded Australian Samantha Stosur logged a second-round victory, beating American Christina McHale 2-6, 6-4, 6-0 Monday, while eighth-seeded Li Na of China handled Spaniard Silvia Soler-Espinosa 6-3, 6-1 to reach the Round of 16.
Martin Bashir resigns from MSNBC over Sarah Palin comments
Exploding whale video goes viral on Internet