Seeded seventh, Sania-Bethanie pair came from a set down to beat the American combination 1-6 6-3 6-0 in one hour and 41 minutes.
The Indo-American duo will next face 11th seeded Rusian-Czech pair of Anastasia Pavlyuchenkova and Lucie Safarova.
Sania had already exited from the mixed doubles event in the opening round. Sania's defeat with her new Swede partner, Robert Lindstedt was shocking as they were given the top billing. They lost to Aisam-ul-haq Qureshi and Cara Black.