The Spaniard, seeded eighth at the Austrian event, was overwhelmed in the opening set but fought back to post a 0-6 7-6 (7/3) 6-4 in two hours and 13 minutes.
It marks Granollers' first ATP Tour title in two years and he admitted Argentinian Monaco made life tough for him at first.
"I definitely didn't start well but he played unbelievable, very solid with almost no mistakes," said Granollers.
"But until you lose the last point, you are still standing and I kept on going."
The Spaniard's luck began to turn midway through the second set with a break of serve for 4-3 and although Monaco won the game back, Granollers came through in the tie-break.
He then raced into a 4-0 lead in the decider and that ultimately proved enough to give him the edge, despite Monaco threatening a late comeback.