Bhupathi and Uzbekistan's Istomin defeated the Austrian-Romanian pair 4-6, 6-3, 16-14 in an hour and 29 minutes to make the last-eight stage.
Saving five break points was key to Bhupathi-Istomin's victory even as they committed seven double faults.
The Indo-Uzbek pair cashed in on both the break chances that came their way.
They will now clash with the second seeded Indo-Pak team of Rohan Bopanna and Aisam-ul-haq Qureshi.
Image: Mahesh Bhupathi
Photograph: Dean Mouhtaropoulos/Getty Images