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.
Jessica Simpson shares three-way kiss with friends in photo
Interpol investigating stolen passports on missing flight