Roger-Vasselin admitted: "Almost everything worked well and we are very happy. We were close to losing in our first match [against Juan Monaco and Horacio Zeballos] and saved one match point in our quarter-final [against Andre Begemann and Martin Emmrich]."
The duo, who is in 16th position in the Emirates ATP Race To London, earned 500 Emirates ATP Ranking points and split $92,200 in prize money.
Bopanna, 34, is now 9-16 lifetime in tour-level finals while 29-year-old Roger-Vasselin improves to 6-1 in title matches.
Murray saved one break point at 30/40 in the fourth game, while Peers saved a set point at 4-5, sudden death deuce with an ace down the middle. In the tie-break, Murray hit a backhand volley into the net at 3-3 and gave Bopanna and Roger-Vasselin an opportunity to clinch the set.
Murray was broken to love at 1-2 in the second set. It proved to be decisive as Bopanna and Roger-Vasselin dropped just four service points in the set to earn the title.
Murray and Peers dropped to a 28-14 match record on the season, which includes three titles.
Murray and Peers share $41,600 and earn 300 Emirates ATP Ranking points for their runner-up finish. Murray, 27, is now 10-6 in finals and Peers drops to 3-1 overall.