Sharapova, also the champion in 2012 and runner-up in 2013, goes on to face Czech 13th seed Lucie Safarova for a place in the quarter-finals.
Safarova made the fourth round for the third time by beating big-serving German Sabine Lisicki 6-3 7-6 (7-2).
Sharapova has a 4-1 record over the 28-year-old Czech, whose only win came in the pair's first meeting in Madrid five years ago.
However, their last clash in Stuttgart in 2014 only went in the Russian's favour after three tiebreak sets.
Former champion Ana Ivanovic reached the last 16 in just 53 minutes.
The Serbian seventh seed, the 2008 winner in Paris, triumphed over 18-year-old Croatian opponent Donna Vekic 6-0 6-3.
Ivanovic won the first seven games before Vekic, the world No.165 and playing in the third round of a major for the first time, stopped the rot and broke for 2-1 in the second set.
But that was as good as it got for the teenager as Ivanovic, watched by German football star boyfriend Bastian Schweinsteiger, swept into a fourth-round clash against ninth-seeded Russian Ekaterina Makarova.
"After my first two matches, I have really started to get a little bit of feeling and groove," said the Serb, who had to come back from losing the opening set in her first two rounds in Paris.
"When you know you are working the right direction, it always gets results."
Makarova reached the last-16 for the second time by defeating doubles partner Elena Vesnina 6-2 6-4.
"I hate having to play my best friend," admitted the 26-year-old left-hander. "It's not a good feeling."
Alize Cornet, the 29th seeded Frenchwoman, needed two and a half hours to defeat 33-year-old Croatian Mirjana Lucic-Baroni 4-6 6-3 7-5 in a match scarred by 85 unforced errors.
Lucic-Baroni made her Paris debut back in 1999 and had made the last 32 by putting out third-seeded Simona Halep in the second round.
Cornet, who knocked Serena Williams out of Wimbledon last year, will be playing in the second week in Paris for the first time.
"It was difficult, she hits the ball very hard," said Cornet.
"I had a terrible start but I came back with courage. It's magical."
Cornet next takes on Elina Svitolina, the 19th seeded Ukrainian who has reached the fourth round of a major for the first time.
Svitolina defeated fellow former French Open junior champion Annika Beck of Germany 6-3 2-6 6-4.
Spanish 21st seed Garbine Muguruza, who beat Serena Williams on her way to the quarter-finals in 2014, knocked out German 11th seed Angelique Kerber 4-6 6-2 6-2.
-AAP
