Sharapova, seeded second this week, routed Garbine Muguruza 6-2, 6-2 without seeing a break point. Sharapova lost just 10 points -- two on double faults -- in her eight games serving.
Sharapova will go against 16th-seeded Sloane Stephens in the third round. Stephens was a 4-6, 6-3, 6-2 winner over Kiki Bertens by saving all three break points she saw in the third set and cashing in two of her own three opportunities.
No. 3-seeded Victoria Azarenka completed the day's schedule with an efficient 6-2, 6-0 romp over Julie Goerges. Azarenka won three-quarters of the points on serve and 65 percent overall.
Fifth-seed Li Na, who lost to Sharapova in last year's Italian Open final, beat countrywoman Zheng Jie 6-3, 6-1 and seventh-seeded Sara Errani escaped a three-set challenge from Christina McHale 5-7, 7-5, 6-2. No. 9-seeded Samantha Stosur beat Peng Shuai 7-6 (7-5), 6-0.
Other seeded winners Wednesday were No. 12 Maria Kirilenko, 13th-seeded Roberta Vinci and No. 14 Dominika Cibulkova, whose 5-7, 6-1, 6-3 win over Melanie Oudin put Cibulkova into the third round against world No. 1 Serena Williams.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys