Bhupathi and his Canadian partner Daniel Nestor, seeded fifth, defeated Romania's Victor Hanescu and Slovak Martin Klizan 6-1 7-6 (8) to enter the third round.
They next face unseeded Italian combination of Simone Bolelli and Fabio Fognini, who shocked 12th seeds Rohan Bopanna and Rajeev Ram 6-2 7-6 (3).
Paes and Elena Vesnina overcame a stiff resistance from unseeded team of Pakistan's Aisam-Ul-Haq Qureshi and Sofia Arvidsson of Sweden in the first round.
The second seeded Indo-Russian pair came from behind to edge past the unseeded rivals 6-7 (8) 6-4 10-7 in one hour and 48 minutes contest.
They next take on Australian pair of Jarmila Gajdosova and Matthew Ebden.
Bopanna crashed out of the men's doubles but advanced to the second round of the mixed doubles.
Bopanna and Chinese Taipei's Su-Wei Hsieh defeated Australian-American pairing of Ashleigh Barty and Jack Sock 6-3 6-3.
The Indo-Taipei pair will now be up against the winner of the match between the Slovak-Italian duo of Daniela Hantuchova and Fabio Fognini and the Russian-American combine of Natalie Grandin and Rajeev Ram.
