The Polish star, who had an early first-round exit from the Summer Olympics, lost the first set before rallying to win 4-6, 6-3, 7-6 (5) and advance to the quarterfinals.
Radwanska trailed repeatedly in the contest, which was delayed by rain, and overcame a 1-4 deficit in the tiebreaker.
No. 10 seed Li Na of China advanced with a 6-4, 6-4 win over Canadian wildcard Eugenie Bouchard. Varvara Lepchenko defeated 12th-seeded Dominika Cibulkova of Slovakia 6-4, 6-4.
The rain delay in Montreal forced suspension of some of the later matches. Top-seeded Victoria Azarenka of Belarus had her match with Tamira Paszek of Austria halted in the first set with the score tied 3-3.
Azarenka will complete the math Friday as will sixth-seeded Angelique Kerber of Germany and seventh-seeded Caroline Wozniaki of Denmark.
Celebrity Families of 2014 [PHOTOS]