Desharnais scored the tying goal with 37 seconds left in the third period and added a goal in the shootout, and the Montreal Canadiens rallied for a 4-3 victory over the Devils.
"We're finding ways to win games," Desharnais said. "They took the lead, and we had to open up things. I just go in there and try to score (in the shootout). (Devils goalie Cory Schneider) opened up his leg, and I put it right there."
Desharnais' tying goal in the third was reviewed by the NHL to see whether he had lifted his stick too high in redirecting the slap shot taken by teammate Brian Gionta.
"I was sure it was a goal," Desharnais said. "I tipped one earlier this year that was a little higher than that, so there was no doubt."
Lars Eller also scored in third period and shootout for Montreal, which also beat the Devils in Montreal on Monday night.
Reid Boucher, credited with an assist on Michael Ryder's goal in the third period, scored for the Devils in the shootout, breaking a string of 20 straight missed chances by the Devils, who are 0-5 in shootouts this season.
The Devils have lost nine straight shootouts, dating back to March 15 in Philadelphia.
Devils coach Pete DeBoer picked Boucher to take the first attempt in the shootout, saying that Boucher "was feeling pretty good about his game and it made sense."
Boucher admitted to being nervous at first, but he seemed to play better and better as the game went on.
"I just heard a couple minutes ago (that the shootout goal snapped a drought)," Boucher said. "We had the lead, and it was unfortunate they scored that goal at the end. I was pretty surprised (to be picked). It's a privilege, and I wanted to capitalize on my opportunity. A quick fake shot, I kind of took a step over and shot a low blocker."
Patrik Elias' unassisted goal at 18:54 had given the Devils a 3-2 edge, but Desharnais scored for Montreal and forced overtime with 37 seconds to go.
Elias had the final chance to tie it for the Devils in the shootout but couldn't beat Canadiens goalie Peter Budaj, who ended the game with 31 saves.
"He's a great shooter," Budaj said. "I was just trying to keep my ground and win that battle. I was able to come up with the big save."
The teams combined for five goals in the third period.
The Devils led 2-1 before Eller scored on a backhand to tie the score at 2-all at 16:10.
Andrei Loktionov and Ryder each scored in the third period to give the Devils a 2-1 lead. Boucher assisted on Ryder's goal.
Gionta scored in the first period to give Montreal a 1-0 lead, and Budaj made it hold until Loktionov scored 4:19 into the third period to tie it at 1-all.
Ryder's seventh goal off a pass from Boucher broke the tie at 9:50.
Loktionov received a pass from Marek Zidlicky before he spun inside and let loose a sailing shot past Budaj for a 1-all tie. Ryder's shot beat Budaj to the far side.
Gionta scored at 10:36 of the first on a pinpoint pass from the outer edge of the left circle by Daniel Briere.
Gionta skated onto the puck at the crease and knocked it past Schneider inside the far post. Seconds before Gionta's goal, Devils rookie defenseman Eric Gelinas had his shot at an open net bang off the right post.
Cam Janssen of the Devils and Brandon Prust of the Canadiens squared off in a fight 2:35 into the first period. Janssen had hit Alex Galchenyuk against the boards before he was challenged by Prust. Both received five-minute penalties for fighting. Montreal held a 13-9 shot advantage in the first.
Boucher got off his first career shot in the opening seconds of the second period, a slap shot that Budaj saved.
The Devils pressed forward in the second period and held a 10-7 shot advantage. Loktionov had a breakaway but was stopped by Budaj. Budaj also made a save on Jaromir Jagr's shot with eight seconds to go.
Ryan Carter was placed on injured reserve by the Devils, who recalled Boucher from Albany (AHL) to take his spot on the roster. Boucher leads the A-Devils with 10 goals and 69 shots.