The seventh seeded Indian pair edged past the Pak-Dutch combination 7-6 (2), 7-6(5) in the quarter-finals of the euro 3,973,695 clay court elite event.
Qureshi was Bopanna's partner in the 2011 season and the duo tasted quite a lot of success together as a team.
Bopanna parted ways with Qureshi to partner Bhupathi, with whom he is expected to play in the London Olympics.
Meanwhile, fifth seed Indo-Czech pair of Leander Paes Radek Stepanek reached the quarter-finals with a 6-3, 6-4 win over their unseeded French rivals Richard Gasquet and Gael Monfils in the second round on Thursday.
Paes and Stepanek now face a tough task as they are up against second seeds Max Mirnyi and Daniel Nestor.
Bhupathi-Bopanna in semis, Paes-Stepanek in quarters in Madrid
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