No. 1 Sharapova needed three sets for a 6-2, 3-6, 6-2 second-round victory over American Bethanie Mattek.
The second-seeded Ivanovic cruised to a second-round 6-4 6-1 rout of unseeded Caroline Wozniacki.
In a major surprise, fifth-seeded Serena Williams of the United States, the only former champion left in the women's draw during a week filled with postponements, lost 6-4, 6-4 to No. 27 seed Katarina Srebotnik of Slovenia after three service breaks and numerous unforced errors.
"I knew it was going to be a tough match, but what can I say?," Williams lamented during a news conference. "She just played unbelievable today."
Williams captured the 2002 French Open crown and this was her earliest exit at Roland Garros since 1999.
She last won a Grand Slam title at the 2007 Australian Open.
Later, Serena's older sister, Venus, the No. 8 seed, lost 7-5 6-3 to Italy's Flavia Pennetta; Poland's Agnieszka Radwanska, the 14th seed, topped 19th-seeded Alize Cornet of France 6-4 6-4; Spain's Carla Suarez Navarro downed Australia's Casey Dellacqua 6-3 6-3 and 10th-seeded Patty Schnyder of Switzerland knocked off France's Emilie Loit 7-6 (7-4) 5-7 6-2.
2014: The Year in Music [PHOTOS]