The sixth-seeded Sharapova needed three hours, 24 minutes for her 100th clay victory, three days after her 27th birthday.
Sharapova, who is bidding to win the tournament for the third time in a row, next faces fellow Russian Anastasia Pavlyuchenkova, who defeated Latvian qualifier Diana Marcinkevica 6-3, 6-2.
Jelena Jankovic, the no. 5 seed, saved four match points to come back and claim a 2-6, 7-6 (8), 6-3 win over German lucky loser Mona Barthel.
Also Tuesday, Svetlana Kuznetsova beat Italian qualifier Gioia Barbieri 6-2, 6-3 and another Russian, Alisa Kleybanova, defeated Croatia's Ajla Tomljanovic 6-2, 6-4.
Spain's Carla Suarez Navarro defeated Russia's Ekaterina Makarova 6-0, 6-4 and Roberta Vinci had a 6-3, 6-2 win over Annika Beck, ensuring the 20-year-old qualifier was the first German knocked out of the tournament.