The 32-year-old Li improved 16-1 this year with a 6-1, 6-4 victory over Aleksandra Wozniak, while Radwanska held off No.22 Alize Cornet, 7-5, 6-3 on the hardcourts at the Indian Wells Tennis Garden.
In a battle of former world No. 1s and Indian Wells champs, seventh- seeded Jelena Jankovic leveled 10th-seeded Caroline Wozniacki, 6-3, 6-1, in 63 minutes. Jankovic titled here in 2010 by beating Wozniacki in the final, while Wozniacki titled here in 2011 and was the runner-up four years ago and last year, when she succumbed to another former No. 1, Maria Sharapova, in the finale at Indian Wells Tennis Garden.
Meanwhile, recent Doha champion Simona Halep held off rising 18th-seeded Canadian Eugenie Bouchard, 6-2, 1-6, 6-4. Bouchard was a surprise Aussie Open semifinalist in January.
Up next for the sixth-seeded Romanian Halep will be Aussie Casey Dellacqua, who advanced via walkover when American Lauren Davis pulled out of the draw on Day 7, citing stomach problems.
Others moving on were 12th-seeded Dominika Cibulkova, 17th-seeded Sloane Stephens and 20th-seeded Flavia Pennetta. Cibulkova, the Aussie Open runner- up, defeated eighth-seeded Petra Kvitova, 6-3, 6-2, Stephens earned a 6-3, 7-5 win over Alisa Kleybanova and Pennetta downed Camila Giorgi, 6-2, 6-1.
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