Williams improved to a 32-2 on the year with a 6-2, 6-2 win over Laura Robson. Williams did lose her serve once in the first set but still took about two-thirds of the points on serve in match.
Robson defeated Venus Williams in a first-round match Monday to earn a second-round shot at Serena Williams.
Qualifier Simona Halep ousted Agnieszka Radwanska, giving the world No. 4 her third loss in four matches. Halep lost her serve at least once in each set but piled up eight breaks against Radwanska.
Also in the second round, No. 8-seeded Petra Kvitova, despite a shaky second set in which she won just nine points, advanced over Sabine Lisicki 6-4, 0-6, 7-5.
Bojana Jovanovski eliminated 10th-seeded Caroline Wozniacki 2-6, 6-4, 7-6 (7-5) in a 3-hour, first-round battle and Carla Suarez Navarro took out 11th-seeded Nadia Petrova 3-6, 6-2, 7-6 (7-1) in a 2 1/2-hour match.
Urszula Radwanska, Agnieszka Radwanska's sister, defeated No. 15-seded Ana Ivanovic 6-3, 2-6, 6-2.
No. 12-seeded Maria Kirilenko topped Anabel Medina Garrigues 6-3, 6-3 while 13th-seeded Roberta Vinci, also played nearly 3 hours, edged Elena Vesnina 6-7 (2-7), 7-5, 6-4. No. 14th Dominika Cibulkova rebounded for a 1-6, 6-2, 6-2 decision over Kristina Mladenovic and 16th-seeded Sloane Stephens ousted Flavia Pennetta 6-3, 6-3.
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