The demonstrative 23-year-old will face Dominika Cibulkova of Slovakia on Saturday in the final WTA tuneup event before the U.S. Open, the final Grand Slam event of the season that starts Monday in New York.
Gavrilova grew up in Russia, moved to Australia when she was 18 and switched her nationality to Australia in December 2015.
The second-seeded Cibulkova beat qualifier Elise Mertens of Belgium 6-1, 6-3 in the afternoon.
Cibulkova is looking for her ninth career title, but her first this season. Gavrilova is looking for the first title of her career.
The 26th-ranked Gavrialva appeared in control throughout the match. Radwanska, ranked No. 10 in the world, could manage just three points during her first two service games and found herself in an early 0-4 hole from which she could not recover.