But Luke Kunin replied for the Preds at 10:12 to lock the game at three apiece and eventually force OT.
The shots were 41-20 for Nashville through regulation.
Just as game looked like it was headed to the shootout, Filip Forsberg scored the winner with 12 seconds left in the extra frame.
The Canadiens will be back in action on Tuesday, when the Tampa Bay Lightning visit the Bell Centre.