Seventh seeds Bopanna and his Chinese partner Jie Zheng became the first pair to enter the last eight after defeating unseeded Swedish-Hungarian duo Johan Brunstrom and Katalin Marosi 7-6(4), 3-6, 6-1 in one hour and 29 minutes.
In the next match on court 12, second seeds Sania partnering Romanian Horia Tecau thrashed American-French duo Eric Butorac and Alize Cornet 6-1, 7-5 in exactly an hour.
Bopanna and Zheng, after winning the first set in a tie-breaker, lost the second after their opponents converted their second break point.
The Asians dominated their European counterparts in the third set, breaking them twice and letting them take home only one game in a 26-minute battle.
Meanwhile, Mirza and Tecau took the first set in 17 minutes breaking their opponents twice. In the second set, Butorac and Cornet fought back to push the set to five-all but the second seeds converted their breakpoint at the right time to take home the set and match.