The Canadiens blew a 2-0 lead against Anaheim, fell behind 3-2, tied it on Brendan Gallagher's second-period goal and won it in the Shootout when Andrei Markov beat Jonas Hiller.
Making his first NHL start in two years, Dustin Tokarski made 39 saves through 65 minutes and, crucially, stopped Saku Koivu in the Shootout.
The Canadiens swept their season series against the team with the most points in the league.
Scoreless OT, but the amazing Brendan Gallagher created a good chance.
On to Dustin Tokarski's first careeer Shootout.
Bonino: Easy goal
Galchenyuk: Backhand saved
DD: Backhand goal!
Palmieri: Never crossed the line!
On to OT
No scoring, but Ryan Getzlaf and Tomas Plekanec hit goalposts.
Shots were 9-7 Canadiens.
Anaheim raised its total of second-period goals to 80 this season.
Tim Jackman got the home team on the board before François Beauchemin scored a bizarre power-play goal: a dump-in along the glass that hit a stanchion and ricocheted past Dustin Tokarski, who had left his net to chase a puck he thought was going into the corner.
Daniel Winnik embarrassed Alexei Emelin and scored to give the Ducks a 3-3 lead.
But wth 37 seconds left in the period, Brendan Gallagher lifted his 16th past Jonas Hiller to make it 3-3.
Anaheim outshot the Canadiens 19-8.
Max Pacioretty took a big hit from Beauchemin and left the game.
As was the case against the Leafs at the Bell Centre, the Canadiens were on the board before their opponent had a shot on goal.
Brian Gionta's 13th came after Tomas Plekanec won a faceoff and skipped past Saku Koivu.
The home team didn't get a shot until the game was 11 minutes old.
But with P.K. Subban off for hooking, Anaheim peppered Dustin Tokarski with eight shots.
He stopped them all, and Max Pacioretty's 30th, off a lovely David Desharnais set-up, made it 2-0.
Despite their early drought, Anaheimoutshot the Canadiens 13-10.
Waiting for Vanek
Well, that was a blockbuster ... and I don't mean the acquisition of Devan Dubnyk.
If the Canadies were playing on the east coast, we might see Thomas Vanek in the lineup tonight.
But they're in California, and the sniper will join the team Thursday in Arizona.
Vanek will wear jersey number 20, most recently worn by Colby Armstrong.
Dustin Tokarski makes his first start in goal for the Canadiens in Anaheim. George Parros faces one of his former teams. Lars Eller is a healthy scratch.
When the Ducks visited the Bell Centre Oct. 24, the Canadiens got power-play goals from Brian Gionta and Rene Bourque in a 4-1 win.
• THN's Ken Campbell likes the Vanek deal (even though he gets the DD line wrong)
• Mathieu Darche's take (in French)