Trailing 2-0 entering the final period, the Sabres knotted the score on goals by Jason Pominville 53 seconds into the frame and by Derek Roy with 7 1/2 minutes remaining in regulation.
Both teams survived shorthanded situations in the overtime, and Thomas Vanek put Buffalo up in the tiebreaker with a first-round tally.
Montreal's Max Pacioretty beat Jhonas Enroth in the second round, but Boyes faked Carey Price and scored in the third.
Enroth made it hold up by stopping Brian Gionta on the Canadiens' last chance, giving Buffalo its fifth straight win over the Habs.
The Sabres' goalie finished with 25 saves to earn the win.
Eric Cole and Pacioretty scored in regulation while Price stopped 30-of-32 shots for Montreal.
Celebrity Families of 2014 [PHOTOS]