"We are trying to move forward and play well going into the playoffs," goaltender Martin Brodeur said. "This is a big win. We didn't play our best game. We were patient in the third, not trying to score right away. We got rewarded by a big goal at the end."
The win guarantees that the Devils won't finish lower than fifth in the Eastern Conference, but it wasn't enough to keep them alive in the division race. The Pittsburgh Penguins captured the crown with a victory over Philadelphia on Wednesday.
The Devils can clinch fourth by winning at Philadelphia on Friday or beating the New York Rangers at home Sunday in the regular-season finale.
"We talked about the home-ice advantage," said Parise, who got a shot at the game winner after Brodeur stopped Glen Metropolit, Phil Kessel, David Krejci and Marco Sturm in the shootout. "That's the thing we need to get. It's an important win for us."
Bruins goalie Tim Thomas had stopped Brian Gionta, Patrik Elias and Jamie Langenbrunner before facing Parise.
Parise skated slowly down the middle, make a deke and lifted a backhander over the Thomas' glove.
"I was watching what the other guys were doing, seeing what Thomas was doing," Parise said. "Gionta was saying he's putting his glove down. I just wanted to put it over it."
Despite the loss, the Bruins inched closer to a playoff spot, earning a point for the sixth straight game (3-0-3) on goals by Dennis Wideman and Milan Lucic. It gave them 92 points, tying Boston with Ottawa for sixth place in the East - one point ahead of eighth-place Philadelphia. All three teams have two games to play.
"It's really up to us to do our job and worry about winning our hockey games," Bruins coach Claude Julien said. "That's where we are at now, and that's why that second point would have been huge."
The loss came a year to the day after Julien was fired by the Devils with three games left in the regular season and replaced behind the bench by general manager Lou Lamoriello.
"It's been a challenge for us to win games in shootouts," Julien said. "Hopefully that point will be big down the road. There is no question the effort was there."
Dainius Zubrus and David Clarkson scored for the Devils, with Clarkson's goal with 5:28 left in regulation forcing an entertaining overtime that featured 10 shots.
Brodeur made two good saves on Zdeno Chara, and Thomas had a nervous glove save on Mike Rupp, snapping his head around to look at the net after the play.
Rupp, who set up both Devils goals, skated behind the goal line and backhanded a pass in front. It went past several players and right to Clarkson for his ninth goal.
While the Bruins dominated play for most of the first two periods, they were lucky to have a 2-1 lead.
Tied at 1 with 7:38 left in the middle session, Zubrus appeared to net his second of the game with a wraparound.
There was no call by the officials, but Thomas reacted in a way that indicated the puck went across the line into the corner of the net.
The played was reviewed in Toronto for several minutes, during which time Zubrus skated over to Thomas and said something that made the goalie smile. Referee Paul Devorski eventually signaled no goal.
A little more than 4 minutes later, Lucic ended an 18-game goal drought by backhanding a shot in front past Brodeur.
Boston had tied it early in the second period when Wideman ripped a shot from the top of the right circle past Brodeur with the Bruins enjoying a two-man advantage.
Zubrus had given the Devils the lead, putting the rebound of Rupp's shot past Thomas 3:14 after the opening faceoff. Thomas failed to control Rupp's shot from the left circle, and Petteri Nokelainen whiffed trying to clear the puck in front.