Fourth seeds Paes and his Czech partner Radek Stepanek sailed past Britain's Jamie Delgado and Australia's Matthew Ebden in straight sets 6-4 6-4 6-3 in an hour and 55 minutes.
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.
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.
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For Paes, unlike his first round encounter which was a keenly contested four setter, the second round battle was a virtual cakewalk.
Again in the final set, the duo got an important service break as they hardly broke sweat before clinching the issue.