The unseeded pair played out of its skin to get the better of its opponents 6-3 3-6 10-4 in the summit-clash of the euro 4,273,775 clay court tournament, the match lasting an hour and 14 minutes at the Monte Carlo Country Club.
The crown is the the first of the season for Bopanna and Cuevas and the third overall for the Indian.
Bopanna had earlier won the Chennai Open in January with Jeevan Nedunchezhiyan but lost in the final of the Dubai Duty Free Tennis Championships, in which he teamed up with Poland's Marcin Matkowski.