Max Pacioretty’s OT winner was his team-record eighth.
The Canadiens took the lead early in the third period on power-play goals by Alexander Radulov and Pacioretty.
But Esa Lindell tied it up late.
John Klingberg’s power-play goal, 12:29 into the second period, gave Dallas a 2-1 lead.
A little past halfway into the first period, Phillip Danault’s superb pass set up Nathan Beaulieu for a shot that beat Kari Lehtonen for the game’s first goal.
Later, Danault backhanded a puck out of harm’s way after Al Montoya was beaten.
With a shade over five minutes left in the period, Tyler Seguin tipped home a point shot to tie it up.
Shots were 42-33 Dallas.
• Nashville’s Weber Tribute