Bopanna and Qureshi lost 4-6, 6-7(3), 2-6 to Juergen Melzer of Austria and Germany's Philipp Petzschner.
Qureshi had become the first Pakistani player to reach the last eight of any Grand Slam event and the quarter-final appearance is also the best-ever Grand Slam performance for his partner Bopanna.
The first two sets witnessed close-fought battle with both the pairs holding their serve, apart from the break in the very first game by the European pair, while the second set went into a tie-break.
However, the Indo-Pak duo were nowhere in the competition in the third set as Bopanna dropped his serve twice -- in the third and seventh games -- to hand over the match to their rivals in an hour and 37 minutes.
Melzer and Petzschner will now be up against seventh seeds Wesley Moodie of South Africa and Belgian Dick Norman, who beat second seeded American brothers pair of Bob and Mike Bryan 7-6(4), 7-6(5), 6-7(3), 7-5 in another quarterfinal match.