The second-seeded former world No. 1 Sharapova took out 26th-seeded former U.S. Open champ and former Roland Garros finalist Samantha Stosur of Australia 6-3, 6-4, while the seventh-seeded former top-ranked star Ivanovic whipped Croatian teenager Donna Vekic 6-0, 6-3 at the year's second Grand Slam event.
The career Grand Slam winner Sharapova topped Stosur in a fourth-round affair in Paris last year.
The Russian star has now won 65 of her last 71 clay-court matches.
This year's Australian Open runner-up Sharapova has appeared in the last three French Open finals, including titles last year and in 2012. She was the 2013 runner-up to Serena Williams.
Sharapova's fourth-round opponent on Monday will be Czech Lucie Safarova.
Ivanovic, the 2008 champ and 2007 runner-up, won the first seven games in her match against Vekic and finished with only 11 unforced errors. The Serbian star is in the round of 16 at a Grand Slam for the first time since last year's Aussie Open.
The 18-year-old Vekic was appearing in her first third-round match at a major.
Meanwhile, ninth-seeded Russian Ekaterina Makarova handled fellow countrywoman Elena Vesnina 6-2, 6-4 and a 13th-seeded Safarova tackled 20th-seeded former Wimbledon runner-up Sabine Lisicki of Germany 6-3, 7-6 (7-2).
The quiet Makarova is trying to reach her seventh Grand Slam quarterfinal in her last 14 majors. She appeared in the semis at the last two Slams -- the U.S. and Aussie Opens.
An upset came when 21st-seeded rising Spaniard Garbine Muguruza took out 11th-seeded German Angelique Kerber, 4-6, 6-2, 6-2.
In other third-round play, 19th-seeded Ukrainian Elina Svitolina beat German Annika Beck 6-3, 2-6, 6-4 and 29th-seeded French favorite Alize Cornet rallied for a 4-6, 6-3, 7-5 win over Croatia's Mirjana Lucic-Baroni, who stunned last year's French Open runner-up Simona Halep on Wednesday.
Cornet is into the fourth round at her home major for the first time in 11 attempts.
"At last, I'm into the second week at Roland. I've been waiting for this for 11 years," she said.