Playing in the first match on Court Philippe Chatrier, the eighth-seeded Stosur dropped her serve in the opening game but then reeled off four straight games to take the lead for good.
“Obviously I thought of last year’s last match,” Stosur said. “It was nice to get out there again and, of course, if you can play on any court here you’d want to play on that one.”
Stosur next plays Simona Halep of Romania, who became the first player to reach the second round by beating Alla Kudryavtseva of Russia 6-2, 6-1 on Court 17.
“I don’t think I have to necessarily prove anything. I think having made semis and a final, I think that kind of proves that I have been able to back it up and it wasn’t a fluke the first time,” Stosur said. “Of course I’d love to go a little bit further this year, but I think it’s more just wanting to achieve that rather than I have to do it because of X, Y, and Z.”
No. 32 Tsvetana Pironkova of Bulgaria also advanced, beating Casey Dellacqua of Australia 7-5, 6-3.
Later, seventh-seeded David Ferrer was to play Jarkko Nieminen of Finland, and No. 14 Stanislas Wawrinka was up against French qualifier Augustin Gensse. On the women’s side, 2009 champion Svetlana Kuznetsova was to face Magdalena Rybarikova.
The French Open is the only one of the four Grand Slam tournaments to start on a Sunday, and there were 32 matches scheduled on eight courts.
Less than an hour before play began, two-time Grand Slam champion Lleyton Hewitt withdrew.
The Australian, who had been one of only five men in the draw with a Grand Slam singles title, has not played March because of foot surgery. He was replaced by Marc Gicquel, one of nine French men playing Sunday.
The four remaining Grand Slam champions in the men’s draw are five-time French Open champion Rafael Nadal, Roger Federer, Novak Djokovic and Juan Martin del Potro.
Djokovic, Federer and Del Potro are all expected to play Monday, while Nadal is scheduled to play Tuesday.