The initial draw had set up a potential all-Williams sister second-round match but Robson squashed that with a 6-3, 6-2 victory over Venus Williams. Robson, despite facing 12 break points, won nearly 60 percent of the points on serve and lost her serve twice -- once in each set.
Robson had three breaks in each set, winning 57 percent of the points when Williams served.
That put her in the second round against Serena Williams, who is 31-2 this year.
Ninth-seeded Samantha Stosur, the only seeded player on Monday's schedule, advanced with a 6-2, 6-3 decision over Hsieh Su-Wei. Like Robson, Stosur had three breaks in each set.
Qualifier Simona Halep ripped Svetlana Kuznetsova 6-1, 6-1 without dropping serve while Sabine Lisicki ousted Mallory Burdette 6-1, 6-2 and Jelena Jankovic stopped Tsvetana Pironkova 6-3, 6-0 by finishing off six of her seven break opportunities.
Also in the first round, Nastassja Burnett beat Alize Cornet 6-2, 6-2; Peng Shuai got by Monica Niculescu 4-6, 6-3, 6-2; Ayumi Morita defeated Sorana Cirstea 6-1, 6-3; Kiki Bertens took out Francesca Schiavone 7-6 (7-5), 6-1; Garbine Muguruza took a seesaw 1-6, 6-0, 6-2 result from Mathilde Johansson; and Melanie Oudin advanced with Ekaterina Makarova retired with Oudin ahead 2-6, 7-5, 4-2.