Sharapova, who lost in this year's Australian Open final, spent little time on the red clay at Roland Garros, completing her rout of Romania's Alexandra Cadantu in 48 minutes. The second-seeded Russian finished with 18 winners to none for Cadantu but had to save three break points.
Earlier, Wimbledon champion Petra Kvitova defeated junior Wimbledon champion Ashleigh Barty 6-1, 6-2. After losing the opening game, Kvitova won six straight in the first set against the 16-year-old Australian wild card and again raced through the second set despite being broken once.
"She has a big serve with kicks and good forehand,'' Kvitova said. "She has very good touch.''
The left-handed Czech won her first Grand Slam title at Wimbledon last year, and then won the WTA Championships. Although she has yet to win a title in 2012, she is seeded fourth in Paris and is expected to go deep into the tournament.
"It was tough out there today,'' Barty said. "I didn't play my best tennis, but she didn't allow me to. I was out there giving it my all, but unfortunately just didn't come out on top today.''
Barty is the youngest player in the draw, one of only eight teenagers entered. The oldest player in the draw, 41-year-old Kimiko Date-Krumm of Japan, lost to 2010 French Open champion Francesca Schiavone of Italy 6-3, 6-1.
Sixth-seeded David Ferrer of Spain and No. 8 Janko Tipsarevic of Serbia advanced in the men's tournament.
Later Tuesday, defending champion Rafael Nadal will begin his quest for a record-breaking seventh title at Roland Garros. On the women's side, 13-time Grand Slam champion Serena Williams is to play.
On Monday, Roger Federer reached another milestone - his 233rd victory in a Grand Slam tournament to equal the Open era record set by Jimmy Connors. His only problem was remembering his opponent in his first victory.
"Well, I should (know), shouldn't I?'' Federer said after defeating Tobias Kamke of Germany 6-2, 7-5, 6-3. "I know it was in Australia, but I can't remember who I was playing.''
He was reminded that it was Michael Chang.
"Oh, was it?'' Federer said, a bit surprised. "Well, that was a beautiful victory, then.''
It started Federer on a career in which he has won a record 16 Grand Slam titles and picked up a slew of other records along the way.
And he's only 30.
"I obviously love the big tournaments,'' Federer said. "I have been so successful for such a long time and to already tie that record - 30 years old is pretty incredible, so I'm very happy.''
Along with Federer, top-ranked Novak Djokovic advanced to the second round on Day 2 of the French Open. Djokovic, who is trying to win his fourth straight Grand Slam title, beat Potito Starace of Italy 7-6 (3), 6-3, 6-1.
Among the women, top-ranked Victoria Azarenka won 12 of the final 14 games and beat Alberta Brianti of Italy 6-7 (6), 6-4, 6-2. Also advancing were defending champion Li Na and No. 3 Agnieszka Radwanska.