Williams, No. 1 in the world and the defending Open champion, dispatched Galina Voskoboeva 6-3, 6-0 in 69 minutes. Later in the afternoon, Azarenka, ranked second, routed Aleksandra Wozniak 6-3, 6-1 in 68 minutes.
Williams had her match postponed because of rain Wednesday but had little trouble with Voskoboeva. Williams took 71 percent of the points when serving and faced one break point. She dropped only nine points in the second set.
Azarenka won the first five games against Wozniak, running her U.S. Open string to 17 consecutive games but then lost three games before closing out the first set. She broke Wozniak's serve seven times in eight receiving games.
Flavia Pennetta pulled off the biggest upset in the tournament Thursday, ousting Italian countrywoman Sara Errani 6-3, 6-1. The fourth-seeded Errani dropped serve six times and won only 38 percent of the points on serve.
No. 6 seed Caroline Wozniacki opened the evening session with a 6-1, 6-2 decision over Chanelle Scheepers. Seventh-seeded Petra Kvitova took out Bojana Jovanovski 6-2, 6-4; No. 8-seed Angelique Kerber advanced with a 6-4, 2-6, 6-3 decision over Eugenie Bouchard; No. 10 Roberta Vinci beat Lucie Safarova 4-6, 6-1, 6-2; 13th-seeded Ana Ivanovic topped Alexandra Dulgheru 6-2, 6-1; and 16th-seeded Sabine Lisicki defeated Paula Ormaechea 6-2, 6-3.
Unseeded winners Thursday included Christine McHale and Yaroslava Shvedova, moving her into a third-round match versus Williams, who also won her first-round doubles match with sister Venus Thursday.
The women's draw got back on schedule with the completion of 24 matches Thursday, eight of them postponed from Wednesday.