Tuukka Rask made 24 saves for Boston (27-10-8), which is 12-0-4 since Dec. 14.
\[WATCH: All Bruins vs. Canadiens highlights\]
"I think we're playing to our identity, in terms of we're hard to play against, we're not going to give up a lot of easy chances," Bruins coach Bruce Cassidy said. "You know, when we do break down, which every team does, our goaltending's been excellent. … I think we're getting contributions from everybody."
The point streak is tied for the sixth-longest in Bruins history; Boston went 15-0-1 from March 2-30, 2014.
The line of David Pastrnak (two goals, one assist), Brad Marchand (two assists) and Patrice Bergeron (one assist) combined for six points.
"I think at the end of the day, if I knew I would have to face them now, I probably would have kept them separate for all those years," said Canadiens coach Claude Julien, who was fired by the Bruins on Feb. 7, 2017.
Max Pacioretty scored his seventh goal in the past seven games for Montreal (19-22-6), which lost to Boston for the third time in eight days.