Williams, who bested Victoria Azarenka in last year's title match, had to shake off some early hiccups to defeat Kazakh qualifier Yulia Putintseva 7-6 (7-5), 6-1.
Fourth-seeded Radwanska, meanwhile, had a much easier time with Bulgaria's Tsvetana Pironkova, downing her 6-2, 6-4.
The news wasn't as good for fifth-seeded Li of China, however, who was bounced 6-3, 6-2 by Madison Keys of the United States.
Also falling by way of upsets Sunday were 10th-seeded Caroline Wozniacki, who tumbled to Kazakh Yaroslava Shvedova 6-2, 6-4, and 12th-seeded Italian Roberta Vinci, who was upended by American Varvara Lepchenko 6-1, 1-6, 6-2.
Other Day 2 winners included sixth-seeded Angelique Kerber, No. 8 seed Petra Kvitova, No. 11 Nadia Petrova, No. 13 Maria Kirilenko, No. 14 Marion Bartoli, No. 15 Dominika Cibulkova and No. 16 Ana Ivanovic.
Video of Victoria’s Secret models trying to 'twerk' hits Instagram
Costly malfunction causes beer flood at Boston-area brewery