Adam Brooks, who was playing in place of an injured Mike Hoffman, and Josh Anderson assisted on Pezzetta's tally.
It was Brooks' first point in a Canadiens uniform.
The Habs took their 2-1 advantage into the final stanza.
Bruce Cassidy's contingent put their scoring prowess on display down the stretch, scoring three unanswered goals in a span of 6:51 before the midway point of the period.
After McAvoy scored the game-tying goal on the power play, Charlie Coyle added two goals of his own to put Boston ahead for good.
Taylor Hall capped the scoring for the home side with an empty-netter.
Montembeault finished the game with 36 saves.
The Canadiens close out their three-game road trip on Tuesday night against the New York Rangers at Madison Square Garden.
Puck drop is scheduled for 7:00 p.m. ET.