Chinese world number two Li was challenged early by Madison Keys before progressing with a 7-6 (7-3) 6-3 victory over the American at the WTA Premier event.
Li, who served seven double faults during her win, saved three set points in the ninth game of the first set.
Keys was left rueing those missed opportunities as Li raced out to a 6-2 lead in the tie-break before easing through the second set.
Li will face Spain's Carla Suarez Navarro in the fourth round after the 15th seed brushed past Estonian 24th seed Kaia Kanepi 6-2 6-1 in an hour.
Like Li, Radwanska was pushed early and recovered to claim a 7-5 6-3 victory over Russian 32nd seed Elena Vesnina.
The Polish third seed and 2012 champion had two set points saved in the 10th game of the opening set but converted at the third time of asking – in the 12th game.
Radwanska recovered from a break down in the second set before grabbing the key break in the eighth game to set up a meeting with Elina Svitolina.
The Ukrainian teenager battled past Czech Barbora Zahlavova Strycova 4-6 6-4 6-1 in two hours and 23 minutes.
Slovakian 10th seed and Australian Open runner-up Dominika Cibulkova edged past French 22nd seed Alize Cornet 7-6 (8-6) 6-4.
Cibulkova will face Venus Williams after the American 29th seed served 11 aces in a 6-4 5-7 6-4 victory over Australian wildcard Casey Dellacqua.
American 17th seed Sloane Stephens produced 37 unforced errors in 55 minutes to be thrashed 6-1 6-0 by Danish 10th seed Caroline Wozniacki.
Wozniacki's fourth-round opponent, Varvara Lepchenko, had a much tougher time of it against Croatian Ajla Tomljanovic.
Lepchenko needed three hours to get past Tomljanovic 6-4 6-7 (4-7) 7-6 (7-2).
Li overcomes tough hurdle at Sony Open
