They won the opening round match in the $1,295,790 hard court event 6-2, 6-7(4), 10-5.
In the quarter-finals they will meet Treat Huey of the Philippines and Briton Dominic Inglot.
Begemann is Bopanna's eighth new partner.
Riding on two breaks, the unseeded Bopanna-Begemann easily pocketed the first set, but their opponents fought back in the second.
Peya-Soares saved all the seven break chances they faced in the second set and succeeded in stretching the match to the tie-breaker.
However, Bopanna-Begemann regrouped and prevailed in the match tie-breaker. They won 77 points to 58 by their opponents.
Somdev loses to Isner
Meanwhile, Indian ace Somdev Devvarman bowed out of the singles, going down in straight sets to eighth seeded American John Isner in the third.
The unseeded Indian lost 5-7, 5-7 to his "good friend" in what was their first encounter on the circuit.
Faced with an opponent ranked more than 100 places above him in the ATP list, Somdev fought well in the opening set, saving as many as six break-points.
But he could never really pile the pressure on Isner, who, in got the crucial break while holding his own serve to pocket the set.
Isner, in fact, did not concede a single break-point in the entire match.
The local favourite stamped his authority in the second set, sending down nine aces while breaking Somdev once out of the three chances he earned to seal the issue.
He will next face Cypriot Marcos Baghdatis in the quarter-finals.
Image: Rohan Bopanna
Photograph: Julian Finney/Getty Images
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