The fourth-seeded Indo-Russian combination dismissed the challenge of American-Belarussian pair 6-2 7-6 (7) in the third round contest yesterday.
It was a good day for Vesnina as she earlier, partnering Sania Mirza, reached the women's doubles semifinals.
Bhupathi-Vesnina may run into the Sania-Rohan Bopanna Indian pair in the mixed doubles semifinals if both the pairs win their respective quarter-finals.
Bopanna and Sania are one step away from making the quarter-finals as they face Czech team of Martin Damm and Renata Voracova in the third round.
Earlier, they scored a 7-5 6-2 victory over Jamie Murray of Great Britain and Jarmila Gajdosova of Australia in the second round.
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