The fourth-seeded pair of Paes and Hingis moved into the final-four after getting a walk-over from the Romanian pair of Simona Halep and Horia Tecau in the last-eight encounter.
Bopanna and his Chinese Taipei partner Yung-Jan Chan though had to battle hard against Su-Wei Hsieh (Chinese Taipei) and Henri Kontinen (Finland).
The second-seeded Bopanna-Chan combine got the better of Hsieh and Kontinen 7-6, 5-7, 13-11 in a 1 hour 50 minute battle on Court 17.
Bopanna and Mergea staved off the third-round challenge from Canada's Daniel Nestor and Edouard Roger-Vasselin of France 6-7, 6-4, 6-3 in a match that lasted for just over 2 hours.
The sixth-seeded pair dished out 10 aces as compared to the three sent down by the Canadian-French pair, which was seeded ninth.
The Indo-Romanian duo will now face Dominic Inglot of Great Britain and Robert Lindstedt of Sweden in the last-eight encounter.
India also saw success in the junior girls section as Karman Kaur Thandi served past Germany's Katharina Hobgarski 6-3, 7-6 in the singles opening round. Thandi will now face Evgeniya Levashova of Russia in the third round.
Even Thandi, 17, was not lucky in the junior girls doubles draws she and Elini Christofi of Greece suffered a first-round defeat at the hands of the Australian duo of Kimberly Birrell and Maddison Inglis 3-6, 5-7.
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