Li, the No. 7 seed, won two-thirds of the points in a 6-0, 6-2 romp over Stephanie Foretz Gacon in a 52-minute match. One of the games she lost came on the only break point she saw Thursday but she cashed in six of her seven break chances.
No. 4-seeded Petra Kvitova had 27 unforced errors but still claimed a 6-1, 6-3 decision over Urszula Radwanska. She won half the points off Radwanska's serve and didn't lose her serve.
A scheduled match for second-seeded Maria Sharapova against Ayumi Morita on Court Philippe Chatrier was postponed due the length of a men's match in which Paul-Henri Mathieu edged American John Isner 18-16 in the fifth set after more than 5 1/2 hours.
Earlier ninth-seeded Caroline Wozniacki defeated Jarmila Gajdosova 6-1, 6-4; Angelique Kerber, the No. 10 seed, beat Olga Govortsova 6-3, 6-2; and 14th-seeded Francesca Schiavone rallied for a 2-6, 6-3, 6-1 decision over Tsvetana Pironkova in matches involving other highly seeded players.
Klara Zakopalova ousted 16th-seeed Maria Kirilenko 6-4, 3-6, 6-3 by getting three breaks in the third set of their 3-hour match. Varvara Lepchenko eliminated 19th-seeded Jelena Jankovic 7-6 (7-4), 4-6, 6-4 in another 3-hour marathon.
Also moving out of the second round were No. 22 Anastasia Pavlyuchenkova, 23rd-seeded Kaia Kanepi and 25th-seeded Julia Goerges.
Unseeded players who earned spots in the third round Thursday were Arantxa Rus, Carla Suarez Navarro, Christina McHale, Yaroslava Shvedova and Nina Bratchikova.
Celebrity Families of 2014 [PHOTOS]