The Sabres coughed up the lead with 5 seconds remaining in regulation when Montreal's David Desharnais scored on a pass from Erik Cole, forging a 2-2 tie for the Canadiens.
Buffalo earned its ninth win in 12 games when Myers blasted a shot from the left circle past Habs goaltender Peter Budaj, helping the Sabres keep their late-season playoff push going.
Buffalo pulled to within two points of idle Washington for the eighth and final playoff spot in the Eastern Conference.
Cole scored and Budaj finished with 33 saves for Montreal.
Swim Week Miami Beach 2014 [PHOTOS]