Bopanna had won his first title of the 2013 season in February when he triumphed at ATP 250 event in Marseille, France with British partner Colin Fleming.
He had also reached the final of Rome Masters with compatriot Mahesh Bhupathi but ended runners-up.
It was a tough battle out there for Bopanna and his partner as the two teams fought tooth and nail, not allowing a single break in the opening set.
The fourth seeds had five break chances but Murray and Peers saved all to stretch the issue to a tie-breaker.
In the second set, Bopanna and Roger-Vasselin finally converted a break chance to get a lead, which they maintained to emerge winners.