The World No.5 duo got the better of the second-ranked team 7-6 (5), 6-7 (5), 10-5 in a pulsating Group B match at O2 arena here.
Bhupathi-Bopanna, fresh from their win in Paris Masters, played their heart out against the Belarusian-Canadian duo, winning the tie in a little less than two hours.
It was a must win match for the Indians, who had lost their opening match to Wimbledon champions Jonathan Marray and Frederik Nielsen before bouncing back in the second against Robert Lindstedt and Horia Tecau.
Bhupathi-Bopanna qualify as the runner-up team from Group B and face the winners of Group A in the last four.
India's Leander Paes and Czech partner Radek Stepanek face the Bryan brothers in their final match in Group A Saturday. The World No.3 unit became the first side to qualify from their pool with a win over Spanish combine of Marc Lopez and Marcel Granollers on Thursday.