Radwanska served three aces and won 76 percent of her first-serve points in the 1 hour, 18 minute match.
No. 11 seed Maria Kirilenko of Russia also advanced without much difficulty, but Tuesday's women's slate was notable for some high-profile departures.
Venus Williams of the United States fell 0-6, 6-4, 6-2 to 13th-seeded Kirsten Flipkens. Williams was playing in her first tournament since losing in the first round of the French Open in May and spending the bulk of summer nursing a lower back injury.
Celebrity Families of 2014 [PHOTOS]