Jagr's score-tying goal late in the first period enabled him to pass Mark Messier.
Adam Henrique, Eric Gelinas and Dainius Zubrus also scored as the Devils reeled off four unanswered goals to take a third victory in four games.
Martin Brodeur made 29 saves in what could possibly be his final NHL appearance in his home town -- the 41-year-old goalie is expected to retire at the end of the season.
Max Pacioretty got the only goal for the Canadiens.
Carey Price turned aside 15-of-18 shots.