The eighth-seeded Indo-Austrian pair fought their hearts out before bowing out with a 6-7 (5) 6-7 (3) 6-7 (4) scoreline against one of the best doubles teams in the world.
Bhupathi has already exited from the mixed doubles with Slovakian partner Daniela Hantuchova.
However, it was a remarkable day for India's Rohan Bopanna as he sealed spot in his first ever Wimbledon semifinals with French partner Edouard Roger-Vasselin.
The 14th seeds knocked out sixth seeded Swede-Canadian combination of Robert Lindstedt and Daniel Nestor with a 7-5 7-6(3) 6-7(4) 6-7(3) 6-2 win in the rain-affected quarter-final, late last night.
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Leander Paes had a mixed day as he advanced to the men's doubles semifinals with Czech Radek Stepanek but suffered a tame defeat in the mixed doubles with Chinese partner Saisai Zheng.
Paes and Stepanek, seeded fourth, carved out a 4-6 6-4 6-3 6-4 win over 11th seeded Julien Benneteau of France and Nenad Zimonjic of Serbia.
In the mixed doubles, 15th seventh seeds Paes and Zheng, lost 3-6 3-6 to unseeded American-French combo of Eric Butorac and Alize Cornet.