Published: May 27, 2012 2:50 PM EDT
Updated: May 28, 2012 6:32 AM EDT

PARIS (AP) - Major champions Sam Stosur and Svetlana Kuznetsova won in straight sets Sunday, quickly making their way into the second round of the French Open on opening day.

The sixth-seeded Stosur, who won last year's U.S. Open and reached the final on the red clay at Roland Garros in 2010, beat Elena Baltacha of Britain 6-4, 6-0 in the first match on the main court.

"It's a bit of an early start, but always nice to get through it now," the Australian said. "You have the whole day and whatever else to recover and, yeah, enjoy."

Kuznetsova won the French Open title in 2009 and the U.S. Open in 2004 but is seeded No. 26 this year. Against Mirjana Lucic of Croatia, she won 6-1, 6-3. The Russian faced little trouble despite being broken twice in the second set.

No. 10 Angelique Kerber of Germany and No. 20 Lucie Safarova of the Czech Republic also advanced to the second round, along with Americans Melanie Oudin and Irina Falconi.

Playing later were seven-time Grand Slam champion Venus Williams and 2008 French Open winner Ana Ivanovic.

None of the top three men was in action, but former major champions Andy Roddick and Juan Martin del Potro were on the schedule.

Top-ranked Novak Djokovic and Roger Federer will be on court Monday, and Rafael Nadal is to begin his attempt for a record-breaking seventh French Open title Tuesday.

Fabio Fognini of Italy became the first man to advance, beating Adrian Mannarino of France 6-0, 7-5, 6-1. No. 21 Marin Cilic of Croatia was next, defeating Daniel Munoz-De la Nava of Spain 6-4, 6-4, 7-5.

Juan Carlos Ferrero, the 2003 French Open champion, also moved into the second round. The Spaniard beat Jonathan Dasnieres de Veigy of France 6-1, 6-4, 6-3.

The French Open is the only Grand Slam tournament that starts on Sunday. The other three all start on Monday.

"I don't think it's too big a deal now that it's more of a proper schedule," Stasur said. "I think the first year there was only a handful of matches, and, yeah, if you were on the schedule then, it really didn't feel like the tournament started. Nobody else was thinking that the tournament had started."

Stosur converted five of her eight break points, and briefly allowed Baltacha back into the match by being broken for the first set at 5-3. The Australian broke right back to take the set. In the second set, Baltacha won only four points on her serve, allowing Stosur to advance easily.

Kuznetsova raced through the first set of her match. After leading 3-0 in the second set, Lucic broke twice to get back to 3-3, but Kuznetsova then won the next three games to take the match.

The 30-year-old Lucic reached the Wimbledon semifinals in 1999, but she is now 11-44 against players ranked in the top 30.