The Russian led 5-0 in the second set and held off a fightback to move into the fourth round where she will play either Zarina Diyas or Andrea Petkovic. Belinda Bencic, 18, reached the fourth round for the first time as she beat American Bethanie Mattek-Sands 7-5 7-5.
Elsewhere, Australia's 22nd seed Samantha Stosur lost 6-2 6-0 to unseeded American Coco Vandeweghe, despite winning the first two games of the match.
Czech sixth seed Lucie Safarova came from one set down to beat Serbia's Aleksandra Krunic 3-6 6-3 6-1.
World number four Sharapova has only made it past the last 16 once in the last eight years but told BBC Sport that she expected a successful tournament this time.
"I made it more difficult for myself in the first set but I felt good in the second set," said Sharapova. "She was not going to away so I was happy I was able to finish it off.
"You expect to go further and on to better things. As the matches get tougher, you have to raise your game and that's why there's only one champion.
"You have to have the belief and I absolutely do. You don't work all these hours in practice to not believe in yourself. I want to be the winner and I will do my best to do so."
Swiss teenager Bencic, seeded 30th and a winner at Eastbourne last week, trailed 5-1 in the first set against Mattek-Sands before winning the next six games.
World number 158 Mattek-Sands, who beat seventh seed Ana Ivanovic, could not cause another upset as Bencic set up a match against either Kristina Mladenovic or Victoria Azarenka next.
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