The fifth seed Indo-American pair had to work hard for a 7-6(3), 4-6, 10-4 victory over the Slovakian-Spanish combo, in an hour and 46 minutes.
They next face winner of the other first round contest between Garbine Muguruza/Maria-Teresa Torro-Flor and Lucie Safarova/Anastasia Pavlyuchenkova.
Image: Sania Mirza and Bethanie Mattek-Sands
Photograph: Julian Finney/Getty Images