Monfils relied on his powerful serve to dominate world number nine Gasquet and clinch the fifth ATP title of his career, the second at the Montpellier hard-court indoor event where he had won in 2010.
"This is unbelievable for me," Monfils told reporters.
"I had some back problems at the beginning of the week and I didn't know if I was going to be able to play, so to now have the trophy is pretty crazy."
The 30th-ranked Frenchman, who has suffered from a series of injuries in the past two years, looks back to his best and now has a 12-2 win-loss record so far this season.
His two defeats have come at the hand of world number one Rafael Nadal, who beat him in the Doha Open final and the Australian Open third round last month.
On Sunday, Monfils looked in control throughout, striking nine aces, and did not offer Gasquet a single break chance.
"I have been elevating my game match after match and I am extremely proud of the way I played today," he said.