The Indian pair overcame a strong challenge from their Australian opponents in the first set to carve out a 7-5,6-4 victory in one one hour and 13 minutes and book their places in the quarter-finals at the Olympic Tennis Centre here on Thursday.
Sania and Bopanna will now take on the British combination of Andy Murray and Heather Watson for a place in the semi-finals.
The two teams were engaged in a neck-to-neck battle in the opening stages before Sania and Bopanna broke their opponents' serve in the ninth game to take a 5-4 lead.
The Australians fought back, breaking Bopanna's serve in the very next game to level the scores at 5-5.
The Indians regained the advantage by breaking Stosur's serve. In the next game, Stosur and Peers gave a stiff fight, saving three set points before the Indians forced another service break to clinch the first set in 36 minutes.
The second set started on a shaky note for the Indians with the Australians stretching Bopanna's serve to duece three times. But Bopanna's powerful service came to his rescue as he responded with an ace on all three occasions to hold serve at 1-1.
The Indians soon took control of the proceedings when a double fault by Peers allowed them to clinch a service break and take a 3-2 lead.
In the next game, Bopanna started off with a double fault before managing to hold serve to consolidate the Indians' lead.
The Australian's started to make more mistakes and gave away easy points on several occasions. They conceded five double faults in the second set as compared to none in the first set.
Six excellent aces and a service break in the 5th game from the Indian pair made it easier for the Indian duo to surpass the Australian duo of Sam and Peers in just 1hour and 13 minutes.
The subsequent games went with the serve before Bopanna held his serve to win the set and the match.
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