Bopanna and his American partner Rajeev Ram saved all the seven breakpoints in the second set to beat Eric Butorac and Paul Hanley 7-6 (8) 6-4.
Only once Bopanna and Ram were broken in the match and they next face Marin Cilic and Lukas Dlouhy.
In the women's event, seventh seeds Sania Mirza and her American partner Bethanie Mattek-Sands defeated Eva Birnerova and Varvara Lepchenko 7-5 6-3 in one bour and 21 minutes.
They will now fight it out with Jarmila Gajdosova and Sabine Katharina Lisicki.
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