Sharapova finished her match, which was suspended Wednesday because of darkness, defeating Tsvetana Pironkova 7-6 (7-3), 6-7 (3-7), 6-0. Sharapova staved off five set points Wednesday in the first set and Pironkova controlled the second tiebreaker to force a third set.
But Sharapova dominated from there, taking just 29 minutes and winning more than two-thirds of the points. She dropped just four points (75 percent) on serve in the set and took 59 percent off Pironkova's serve.
Azarenka, with one of the last matches of the day, blitzed Romina Oprandi 6-2, 6-0 in a brisk 51 minutes. Azarenka cashed in 4-of-5 break chances while wining 57 percent of the points when receiving serve.
Williams rolled by Melinda Czink 6-1, 6-4, piling up 10 aces and 22 winners. She ran through the first set in 20 minutes, winning 25-of-34 points in the set. On the day, Williams claimed 37-of-44 points on serve, an 86 percent success rate.
Defending champion Petra Kvitova won the first 10 games in her Thursday match in a 6-0, 6-4 victory over Elena Baltacha. She seemed to lose her focus after going up 4-0 in the second set before settling down and advancing.
However, qualifier Mirjana Lucic ousted ninth-seeded Marion Bartoli 6-4, 6-3. Bartoli landed just 53 percent of her first serves and had 10 double faults, which helped Lucic finish with three breaks.
Varvara Lepchenko beat No. 31-seeded Anastasia Pavlyuchenkova 7-6 (7-4), 6-4 in the day's other upset on the women's side.
Ana Ivanovic, the No. 14 seed, claimed a 6-3, 7-6 (7-3) decision over Kateryna Bondarenko.
Other second-round results Thursday saw No. 20 Nadia Petrova, 21st-seeded Roberta Vinci, 22nd-seeded Julia Goerges, No. 24 Francesca Schiavone, No. 25 Zheng Jie and 28th-seeded Christina McHale advance.
Unseeded women headed to the third round include Klara Zakopalova, Yanina Wickmayer, Tamira Paszek and Yaroslava Shvedova.