Montreal drove Tuukka Rask from the game by putting three goals past him on 17 shots and the Canadiens went on to snap the Bruins' four-game win streak.
Defenseman Alexei Emelin scored his first goal of the season and the seventh of his three-year career just 2:16 into the contest to get Montreal going.
The only goal given up by Budaj came from David Krejci on a deflection with 4:22 to go in the first stanza. Budaj finished with 34 saves.
Chad Johnson replaced Rask and allowed one goal on 16 shots.