Radwanska -- who placed second in last year's event -- breezed past Olga Govortsova 6-2, 6-0 at Autotron Rosmalen.
Two other main draw matches were held on the tournament's first day.
Anabel Medina Garrigues of Spain had little trouble with Kiki Bertens of the Netherlands, besting her by a 6-1, 6-2 margin, while Dutchwoman Michaella Krajicek downed Silvia Soler-Espinosa of Spain 7-5, 6-4.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys