The seventh seeded Indians carved out a hard-fought 7-6(7) 6-4 in one hour 23 minutes in the quarter-finals of the USD 3,531,600 hard court event.
They next face unseeded British pair of Colin Fleming and Ross Hutchins.
Saving five breakpoints, including four in the opening set, proved vital in Bhupathi and Bopanna's win.
Leanader Paes and his partner Radek Stepanek, seeded fpurth, are also due to play their quarter-final later in the day.
They are up against unseeded combo of Canadian Milos Raonic and Austrian Jurgen Melzer.