The Canadiens became the second team in the Eastern Conference behind Pittsburgh to wrap up a post-season berth.
Montreal scored the game's first four goals and jumped past Boston into the top spot in the Northeast Division with 57 points.
Bourque and Alex Galchenyuk scored in the opening period and Brendan Gallagher and Andrei Markov produced second-period goals for Montreal.
Peter Budaj was called on to make only 14 saves and had his shutout spoiled by Brian Flynn, who scored shorthanded 6:45 into the third.
Ryan Miller allowed four goals on 32 shots before being removed in the third period for Jhonas Enroth.
Buffalo, six points out of the final playoff spot in the Eastern Conference, has lost two in a row.
Celebrity Families of 2014 [PHOTOS]