The Russian squandered an early break in the first set before breaking again in the 11th game and then fended off break point before closing out the opener in 58 minutes.
Sharapova saved two break points in the second game of the second set before taking control and reeling off four straight games from 3-2 down to claim victory in one hour and 40 minutes.
"I thought it was a tough one - she's a quality player, capable of playing some really good tennis," Sharapova said of her opponent.
"She's dangerous. She's beaten top players in Grand Slams before and has a really solid game with a lot of variety, and she can hit the ball as well. She's really tough.
"There are a few things I want to improve on, but I was happy I got through on not a great day."
Sixth seed Sara Errani cruised into the fourth round, dismissing Sweden's Johanna Larsson 6-3 6-1 in 81 minutes.
Russian number 13 seed Maria Kirilenko defeated American qualifier Mallory Burdette 6-3 4-6 6-2.
Czech number 19 seed Klara Zakopalova defeated Slovakia's Dominika Cibulkova 6-4 7-5.
Poland's Agnieszka Radwanska was a 6-7 (3/7) 6-3 6-4 winner over Romania's Sorana Cirstea and Spain's Lara Arruabarrena-Vecino won 2-6 6-4 6-4 against Italy's Roberta Vinci.
And Czech fifth seed Petra Kvitova defeated Ukraine's Lesia Tsurenko 6-2 7-5 (7/5), while France's Marion Bartoli cruised past two-time grand slam winner Svetlana Kuznetsova of Russia 6-4 6-3.