Updated

Paris, France (SportsNetwork.com) - Fourth-seeded Simona Halep, former Wimbledon champion Petra Kvitova and sixth-seeded former world No. 1 Jelena Jankovic all reached the third round at the French Open on Thursday.

Recent French Open runner-up Sara Errani of Italy also advanced on Day 5, as did former champ Svetlana Kuznetsova of Russia.

The Romanian Halep humbled Brit Heather Watson 6-2, 6-4, while the fifth- seeded left-handed Czech star Kvitova handled New Zealand's Marina Erakovic 6-4, 6-4 and the veteran Serbian star Jankovic eased past Japan's Kurumi Nara 7-5, 6-0.

Up next for Halep will be Spaniard Maria-Teresa Torro-Flor, while Kvitova will face the former top-five star Kuznetsova and Jankovic will take on Romanian Sorana Cirstea.

"There are still a lot of great players in the draw, every round is going to be tough," said Jankovic. "The opponents get more and more difficult."

The 10th-seeded 2012 Roland Garros finalist Errani eased past German Dinah Pfizenmaier 6-2, 6-4, while the 27th-seeded Kuznetsova, who captured the 2009 title and was the French Open runner-up in 2006, defeated rising Italian Camila Giorgi 7-6 (7-5), 6-3.

American Sloane Stephens, seeded 15th, dropped only four games in a 6-1, 6-3 victory over Slovenian Polona Hercog.

In other action involving seeds on the famed red clay, Israeli Julia Glushko took out No. 21 Belgian Kirsten Flipkens 6-4, 3-6, 6-4; No. 22 Russian Ekaterina Makarova tackled American Coco Vandeweghe 6-4, 6-3; No. 23 Czech Lucie Safarova got past Aussie Casey Dellacqua 6-1, 5-7, 6-3; Dutchwoman Kiki Bertens knocked out No. 24 Russian Anastasia Pavlyuchenkova 5-7, 6-4, 3-0, retired; a No. 26 Cirstea brushed aside Brazilian Teliana Pereira 6-2, 7-5; and No. 28 German Andrea Petkovic topped Swiss Stefanie Voegele 6-2, 4-6, 6-2.

Also on Thursday, France's Kristina Mladenovic snuck past American Alison Riske 7-6 (7-5), 3-6, 6-3; Spaniard Silvia Soler-Espinosa dropped Belgian Yanina Wickmayer 6-2, 6-4; France's Pauline Parmentier overcame Kazakhstan's Yaroslava Shvedova 1-6, 6-3, 6-3; Argentine Paula Ormaechea came back to best Romanian Monica Niculescu 2-6, 7-5, 6-2; and Spaniard Maria-Teresa Torro-Flor held off Slovak Magdalena Rybarikova 6-2, 2-6, 6-2. Soler-Espinosa was a runner-up in her first-ever WTA final last week in Strasbourg, France.