Former champion Svetlana Kuznetsova and Samantha Stosur were among the early winners at the French Open on Sunday in Paris.

The 26th-seeded Kuznetsova, the 2009 women's champ, cruised past Croatia's Mirjana Lucic 6-1, 6-3 at the world's lone clay-court Grand Slam event.

Stosur, the sixth seed and reigning U.S. Open champ, handled Elena Baltacha of Britain 6-4, 6-0. Stosur finished runner-up at Stade Roland Garros in 2010.

Czech Lucie Safarova, the No. 20 seed, also advanced by defeating Anastasiya Yakimova of Belarus 6-2, 6-0.

Americans Melanie Oudin and Irina Falconi posted first-round victories. Oudin took down Johanna Larsson of Sweden 6-3, 6-3, while Falconi beat Edina Gallovits-Hall of Romania 3-6, 6-3, 6-1.

Ana Ivanovic, the 2008 women's winner, is also on the docket for Sunday, along with 2002 finalist Venus Williams. The 13th-seeded Ivanovic will square off against Spain's Lara Arruabarrena-Vecino, while Williams will face Argentina's Paula Ormaechea.

Li Na became the first-ever Asian Grand Slam winner, male or female, by besting then-reigning champion Francesca Schiavone in last year's French Open finale. Schiavone became the first-ever Italian woman to capture a major title by beating Samantha Stosur in the 2010 final here.

The 2012 Roland Garros champ will pocket $1.57 million.