Williams, No. 3 in the world, lost only three games win her first-round match and followed that with a 6-2, 6-2 romp in the second round over Alize Cornet in about an hour.
Williams won 78 percent of the points on serve and didn't face a break point.
Sharapova cited a shoulder injury in withdrawing. She pulled out of an exhibition last month for the same injury, and her availability for the Australian Open later this month is unknown.
Daniela Hantuchova outlasted fifth-seeded Sara Errani 4-6, 6-1, 7-5 over a 2 1/2-hour, second-round match. There were a total of nine breaks in the 12-game third set, with Hantuchova winning more than 60 percent of the points off Errani's serve in the set.
Qualifier Ksenia Pervak won a third-set tiebreaker in beating Urszula Radwanska 3-6, 6-2, 7-6 (8-6).