The seventh seeded Indians got the better of the American-British unseeded combo 7-6 (9) 6-4 in an hour and 16 minutes.
Bhupathi and Bopanna, who had got a first round bye, converted just one out of two breakpoints to walk away with the match comfortably.
They will next take on the winners of another second round match between Tomas Berdych and Nenad Zimonjic and second seeds Max Miryni and Daniel Nestor.