Azarenka got by Jamie Hampton 6-4, 4-6, 6-2 in a match that took more than 2 hours. Hampton had 41 winners but also 47 unforced errors, which accounted for nearly half of the 100 points Azarenka won in the match.
Azarenka cashed in seven of her eight break-point opportunities and won more than half (49-of-96) of the points off Hampton's serve.
Williams, the No. 3 seed, beat Ayumi Morita 6-1, 6-3 in 66 minutes. Williams won the last five games of the first set and the last six of the match. Morita had a break of serve -- the first suffered by Williams in the tournament -- and led 3-0 in the second set but Williams was too strong.
Williams won 63 percent of the points overall and nearly 70 percent on serve. During the match she uncorked a serve of 128.7 mph -- the fifth fastest in women's tennis history.
Unseeded Elena Vesnina ousted 16th-seeded Roberta Vinci 4-6, 7-6 (7-4), 6-4 in more than 2 1/2 hours. Each player had four breaks and Vesnina won only one more point (103-102) overall, but a pair of breaks in the third set allowed her to advance to a fourth-round match versus Azarenka.
No 10-seeded Caroline Wozniacki had just five winners, dropped serve five times and won just more than half the points on serve but still beat Lesia Tsurenko 6-4, 6-3. Wozniacki had seven breaks and won two-thirds of the points receiving serve. Tsurenko hurt her own cause with 48 unforced errors -- matching the number of points she won.
The other fourth-round pairing in this half of the draw has 29th-seeded Sloane Stephens taking on unseeded Bojana Jovanovski. Stephens, yet to drop a set in the tournament, beat Laura Robson 7-5, 6-3 and Jovanovski topped Kimiko Date-Krumm 6-2, 7-6 (7-3) Saturday.