Radwanska, Kvitova and Wozniacki, the top three seeds for the final tune-up before Wimbledon, combined to win just one set -- by Wozniacki in an extended tiebreaker.
Radwanska, the No. 1 seed, was routed by Tsvetana Pironkova 6-2, 6-4 in 71 minutes. Radwanska had beaten Pironkova six of the seven times they had met but won just more than half the points on serve and lost her serve four times Tuesday.
Ekaterina Makarova topped the second-seeded Kvitova 7-5, 6-4 by piling up five breaks while Christina McHale stopped No. 3-seed Wozniacki 6-1, 6-7 (7-9), 6-4. McHale broke Wozniacki's serve six times.
Fourth-seeded Marion Bartoli, who beat Kvitova in last year's tournament final, played more to form, defeating Sorana Cirstea 6-2, 6-2. Bartoli had eight double faults but still won two-thirds of the points on serve.
No. 5-seeded Angelique Kerber was a 3-6, 6-0, 7-5 winner over Elena Vesnina; seventh-seeded Lucia Safarova squeaked by Timea Babos 3-6, 6-3, 7-6 (8-6); and No. 9-seeded Petra Cetkovska got by Andrea Hlavackova 3-6, 6-2, 6-1.
Other first-round winners Tuesday were Stephanie Dubois, Heather Watson, Klara Zakopalova and Anastasia Pavlyuchenkova.