"We started off slow and it was tough to come back from," said Clarkson. "But I think these guys showed what we're made of tonight. This was a good win."
Trailing by a goal entering the third, the Devils tied the game 6:11 in as Alex Ponikarovsky blasted a shot on net from the right circle that Zubrus tipped in.
New Jersey then took the lead late in the game. Andy Greene was able to poke a clear back into the zone before the puck crossed the blue line and it went to Patrik Elias, who fired a pass to the slot where Ilya Kovalchuk took over. Kovalchuk wound up for a shot and it was blocked, but it took a trip over to the right side where Parise shot it in.
Clarkson scored with the net empty in the final minute of play for his 19th of the season.
Montreal scored two goals in the first 10 minutes to take a 2-0 lead.
The first goal came 4:11 in when Rene Bourque threw his own rebound on net from a sharp angle at the left side that hit off of Desharnais and went in.
At the 9:23 mark, Yannick Weber sent a shot from the right point that Brodeur stopped, but Kostitsyn was all alone in front to spin in the rebound past the outstretched right leg of Brodeur.
New Jersey then used its timeout and it appeared to work as Parise scored on a wrister from the top of the left circle on the fly just 1:13 later.
Just 1:35 in while shorthanded, Montreal made it a 3-1 game as Tomas Plekanec came in on a breakaway that Brodeur made a nice right pad save on, but Darche followed up and jammed the puck in.
The Devils, though, did score on their next power play as a bouncing shot from Kovalchuk at the left point saw the puck hit off of Clarkson and slip past Price with 6:17 to play in the second.
New Jersey plays in Philly on Saturday...Montreal hosts Washington on Saturday...New Jersey has taken two of three from Montreal this season...New Jersey went 1-for-4 on the power play while Montreal was 0-for-3.