Updated

Paris, France (SportsNetwork.com) - Petra Kvitova and Svetlana Kuznetsova were women's winners Tuesday at the French Open, but the former Grand Slam champions were each tested in their openers at Roland Garros.

Kvitova, the fourth seed and a two-time Wimbledon champ, gutted out a 6-4, 3-6, 6-4 win over New Zealand's Marina Erakovic, while Kuznetsova, the 2009 French Open champ and 2006 runner-up, also went the distance in a 6-1, 4-6, 6-2 triumph over Kiki Bertens of the Netherlands.

Kuznetsova, seeded 18th this year, has reached the quarterfinals each of the last two years in Paris. She avoided what would have been a fourth straight first-round exit at a major, having been eliminated in her openers at this year's Australian Open and last year's U.S. Open and Wimbledon.

Kvitova, meanwhile, has struggled on the famed red clay in the French capital. She has advanced past the fourth round just once in six previous visits with a semifinal appearance in 2012. The Czech star did win a French Open tune-up on clay earlier this spring, beating Serena Williams in the semifinals and Kuznetsova in the title match at Madrid.

The top-seeded Williams, a two-time French Open champ, will open her Paris fortnight later today against Czech veteran Andrea Hlavackova.