Third-seeded Kaia Kanepi of Estonia and No. 4 Petra Kvitova of the Czech Republic won their first-round matches in straight sets at the Open Gaz de France on Tuesday.
Kanepi broke Latvian Anastasija Sevastova's serve twice in the second set in a 7-6 (5), 6-2 win, while Kvitova had five aces in a 7-5, 6-4 win over Vesna Manasieva of Russia.
No. 8 Dominika Cibulkova of Slovakia also joined them in the second round. Her win was easier as she handled qualifier Ana Vrljic of Croatia 6-0, 6-2, breaking her opponent's serve five times.
The top-seeded Kim Clijsters needs to reach the semifinals to take the No. 1 ranking from Caroline Wozniacki of Denmark and plays Kristina Barrois of Germany in the second round on Wednesday.
Clijsters, the Australian Open champion, won this tournament in 2004.
''To come back to a place you've only been to once and done well ... it's always nice to go back and see what it's like and how things have changed,'' Clijsters said.
Also advancing with first-round wins were American Fed Cup pair Melanie Oudin and Bethanie Mattek-Sands, Czechs Barbora Zahlavova Strycova and Klara Zakopalova, Australia's Jelena Dokic and Slovakia's Kristina Kucova.
Oudin rallied to beat Vera Dushevina of Russia 7-5, 5-7, 6-2; Strycova won 7-6 (5), 6-3 against Bulgaria's Tsvetana Pironkova; Zakopalova defeated Switzerland's Timea Bacsinszky 6-3, 6-3, and Mattek-Sands routed Spain's Carla Suarez Navarro 6-0, 6-3 in less than an hour.
Mattek-Sands will face second-seeded Maria Sharapova of Russia in the next round, while Oudin plays Cibulkova.
Djokic lost her serve twice but fired 11 aces to overcome Lucie Safarova of the Czech Republic 4-6, 6-3, 6-4.
Kucova dropped her serve four times and had to save a further eight break points in a marathon 4-6, 6-3, 7-6 (1) win over Ekaterina Makarova of Russia.
