Eight seeded Indo-Austrian pair of Bhupathi and Julian Knowle came from a set down to get the better off Nicholas Monroe of the US and German Simon Stadler 3-6 6-4 6-4 6-2 in a tough battle that lasted for two hours and 22 minutes.
They will now take on the Canadian pair of Jesse Levine and Vasek Pospisil.
Bopanna and his French-partner Edouard Roger-Vasselin had to fight hard before prevailing over Daniel Brands and Lukas Rosol in a gruelling five setter of three-hour duration.
Bopanna and Roger-Vasselin pipped the German-Czech combination by 6-3 5-7 7-6 (7-4) 6-7 (8-10) 6-4 in a second round encounter to set up a clash against the third seed pair of Austria's Alexander Peya and Bruno Soares from Brazil.
In more good news for India, the sixth seed Indo-US pair of Sania Mirza and Liezel Huber defeated the Italian-German pair of Flavia Pennetta and Andrea Petkovic 7-6, 3-6, 6-2 to advance to the third round of the women’s doubles.
They now face the Japanese-South African duo of Shuko Aoyama and Chanelle Scheepers in the third round.
Mirza-Huber took the opening set via a tough tiebreaker. Pennetta and Petkovic, however, bounced back to square the match at a set apiece. The Indo-US duo held their nerve to take the decider 6-2.