Bopanna and Uruguay's Pablo Cuevas shrugged off a surprise first set lapse to regroup and beat American pair of Bradley Klahn and Scott Lipksy 1-6, 6-3, 6-4 in the opening round of the men's doubles.
They will take on the Italian team of Simone Bolelli and Fabio Fognini in the second round.
In the women's doubles, Mirza and her Chinese partner Shuai Peng overcame the challenge of Croatian team of Petra Martic and Donna Vekic 6-4, 6-1 in their first round match.
It took the Indo-Chinese pair just 55 minutes to cross the first hurdle.
Mirza and Peng broke their rivals four times but also dropped their serve once in the match.
They next face Slovakia's Jana Cepelova and Magdalena Rybarikova.
File Image: Sania Mirza in action.
Photograph: Action Images/Lee Yaocheng/Livepic/Reuters
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