The fifth seeds beat the Slovakian-Serbian pair 3-6, 6-2, 10-5 in the second round at Melbourne Park.
Bhupathi-Petrova now await the winner of the match between Leander Paes and Elena Vesnina and Jarmila Gajdosova and Matthew Ebden.
Sania Mirza and Rohan Bopanna had made the mixed doubles quarters with different partners Monday.