Alex Galchneyuk was the Overtime hero, blasting a one-timer past Cory Schneider on a power play.
John Moore’s blueline shot gave NJ a 2-0 lead 2:38 into the third period.
But 11 seconds later, Alexander Radulov’s 15th got the Canadiens on the board.
Travis Zajac’s power-play goal made it 3-1, but Max Pacioretty scored his 30th 43 seconds later.
And with Al Montoya on the bench, Pacioretty made it 3-3 at 18:08.
The first period was 19 seconds from being over when Kyle Palmieri took advantage of soft Canadiens D-zone play to beat Montoya from close in.
Shots were 37-33 Devils.