Radwanska defeated Maria-Teresa Torro-Flor 6-4, 7-5 behind five service breaks. Radwanska took nearly half the points off Torro-Flor's serve in posting the five breaks in 11 receiving games.
Torro-Flor had three breaks of her own but managed one less in each set than Radwanska.
No. 3-seeded Alize Cornet won 60 percent of the points on serve and 55 percent when receiving in a 6-1, 6-3 decision over Nina Bratchikova. She had six breaks in Bratrchikova's eight games serving.
Alexandra Panova, the No. 7 seed, rallied for a 4-6, 6-2, 7-5 win over Jarmila Gajdosova. Panova had seven aces and won 65 percent of the points on serve.
Also Monday, Lara Arruabarrena-Veci routed Jana Cepelova 6-1, 6-2 in 62 minutes and Sabina Sharipova topped Vlada Ekshibarova 6-4, 7-5 in a battle of Uzbek wild-card entrants.
Celebrity Families of 2014 [PHOTOS]