Monfils scored a 7-6 (7-5), 7-5 decision over American James Blake in a match-up of former Top 10 players at River Oaks Country Club in Houston.
In other Day 1 play, American Tim Smyczek dispatched Frenchman Josselin Ouanna 6-1, 6-2.
Monday's only other main draw singles match saw American wild card Rhyne Williams defeat Argentine Guido Pella 7-5, 7-5.
Megyn Kelly: Santa Claus and Jesus are both white men
Wisconsin business offering 'therapeutic cuddling' forced to close