Lars Eller also scored in third period and shootout for Montreal, which also beat the Devils in Montreal on Monday night.
Rookie Reid Boucher, making his NHL debut, scored for the Devils in the shootout, breaking a string of 20 consecutive missed chances by the Devils, who are 0-5 in shootouts this season.
Patrik Elias’ unassisted goal at 18:54 had given the Devils a 3-2 edge, but Desharnais redirected a slap shot by Brian Gionta to score at 19:23 for Montreal and force overtime.
RANGERS: Just two days after surprisingly watching from the bench for a second consecutive game, No. 1 goalie Henrik Lundqvist agreed to a long-term contract extension with New York on Wednesday.
Lundqvist, in the final season of a six-year, $41.25 million deal, agreed to a seven-year contract reportedly worth $59.5 million.
His salary-cap charge would rise from $6.875 million to $8.5 million and make him the NHL’s highest-paid goalie.
More importantly, it should keep him starring on Broadway.
“About eight months ago I sat down for the first time with my family and my agent and kind of discussed my future,” said Lundqvist, who said he wants to bring a Stanley Cup to New York and end his career with the Rangers.
BLUE JACKETS: Placed goaltender Sergei Bobrovsky on injured reserve with a groin strain that will sideline him for four to five weeks.
The Vezina Trophy winner as the NHL’s top goalie last season was injured during the third period of Tuesday night’s 1-0 home victory over Tampa Bay.
He was hurt while making a spectacular glove save on a breakaway by J.T. Brown. After making the catch, Bobrovsky fell to the ice with his legs spread, his left leg jammed into the goal post. He had to be helped off the ice.