The second-seeded Russian breezed to a 6-2, 6-1 rout of Taiwan's Hsieh Su-Wei 6-2, 6-1, needing just 54 minutes on Court Lenglen at Stade Roland Garros.
She now goes on to face 19-year-old Canadian Eugenie Bouchard, who moved in with a 6-1, 7-6 (7-2) win over Bulgarian Tsvetana Pironkova.
The fourth-seeded Radwanska downed Shahar Peer of Israel 6-1, 6-1 in 57 minutes.
Radwanska, last year's Wimbledon runner-up who has won two tournaments this year, has never advanced beyond the fourth round at the French Open, but last year made it to the third round.
Her sister Urszula downed Venus Williams, the 30th seed, in the final match Sunday, 7-6 (7-5), 6-7 (4-7), 6-4.
Sixth-seeded Li, the 2011 champion, notched a 6-3, 6-4 win over Anabel Medina Garrigues of Spain, and will next face American Bethanie Mattek-Sands.
Elsewhere on Day 2, No. 8 Angelique Kerber got past fellow German Mona Barthel 7-6 (8-6), 6-2 and 10th-seeded Caroline Wozniacki of Denmark ended a five-match dry spell with a 6-3, 6-2 triumph over Briton Laura Robson.
Seventeenth-seeded American Sloane Stephens, Russian Svetlana Kuznetsova, 21st-seeded Belgian Kirsten Flipkens, American Melanie Oudin, Francesca Schiavone and 29th-seeded American Varvara Lepchenko moved on as well.
2014: The Year in Music [PHOTOS]