The unseeded Indo-French team defeated the Serbian rivals 6-3 6-3 in the opening round of the USD 1,785,500 hard court event.
They next face Polish fourth seeded pair of Mariusz Fyrstenberg and Marcin Matkowski.
Rohan Bopanna and his American partner Rajeev Ram had also reached the quarter-finals after shocking second seeds Jean-Julien Roger and Aisam-ul Haq Qureshi in their opening round.
Somdev Devvarman had bowed out of the singles event after suffering defeat at the hands of world number seven Argentine Jual Martin del Potro.
If Bhupathi and Bopanna win their next matches with their respective partners, they will clash in the semifinals and it will ensure that at least one Indian will compete for the title in the summit clash.