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.