The great Martin Brodeur was beaten three times on a mere 17 shots.
Rene Bourque's sixth goal of the season, in the second period, erased a 1-0 lead fashioned by Steve Bernier in a first period dominated by the visitors.
After red-hot Max Pacioretty's 10th made it 2-1, Michael Ryder tied it up six minutes into the third period.
Then a bizarre sequence of bad passes ended with Alex Galchenyuk – benched for the third period against Toronto on Saturday – using his great hands to tap the winner past Brodeur.
Carey Price made 27 saves and preserved his stellar 2.00 GAA.
The Canadiens' penalty killers threw another shutout at NJ's three power plays.
Kid bags winner
Against Toronto on Saturday, Alex Galchenyuk spent the third period on the Canadiens' bench.
Against New Jersey, the 19-year-old scored the winning goal.
Martin Ryder had tied the game at 2-2.
.600 save percenatge
The great Martin Brodeur faced five shots in the second period.
Two went in.
Rene Bourque's sixth got the Canadiens on the board.
Then the home team went without a shot on goal for more than eight minutes before the red-hot Max Pacioretty blasted a power-play feed from Andrei Markov past Brodeur.
Shots were11-5 for the visitors ... exactly what they were in the first period.
New Jersey outshot the home team 11-5 and got the only goal of the first period when Steve Bernier tipped home Marek Zidlicky's point shot.
The Devils had wide-open looks from the slot all through the period, as the Canadiens stumbled around their own end, unable to win puck battles.
Michel Therrien will have much to say between periods.
Martin Brodeur grew up in St. Leonard, a multi-ethnic district of Montreal.
His late father, Denis Brodeur, was a photographer for the Journal de Montréal.
But through the course of a first-ballot-cinch Hall of Fame career, the New Jersey Devils goaltender has displayed little nostalgic affection for his hometown ... or at least for fans of the local hockey team.
Brodeur's lifetime statistics against the Canadiens: 44-18-6, 9 shutouts,1.83 goal-againstaverage, .930 save percentage.
And some of Brodeur's best performances are on Montreal ice.
So despite recent stellar play by NJ heir apparent Cory Schneider, who posted a shutout of Buffalo on Saturday, the homeboy starts when New Jersey visits the Bell Centre Monday night.
The Canadiens begin a busy week: four games in six nights, including a return visit to New Jersey on Wednesday and Boston at the Bell Centre on Thursday.
Michaël Bournival draws back in for George Parros and will play with Brandon Prust and Travis Moen.