Callahan provided the lead 34 seconds in, Derek Stepan added a goal in the first period, and Taylor Pyatt snapped a long drought in the second for the eighth-place Rangers, who are inching closer to a playoff berth.
"It's always nice to beat them," said Brad Richards, who had two assists. "It was a big win for us. They're out now, but that's not why we were playing. We were playing because we need to stay alive. Now we're down to nine teams, so the odds are better."
Of the teams behind the Rangers, only Winnipeg can catch them. New York is even in points with seventh-place Ottawa, but the Senators have four games remaining -- one more than the Rangers. Winnipeg is three points behind with three games left.
New York has won three straight and is 8-2-1 in its last 11. The Rangers aren't looking too far ahead. After a trip to Florida and Carolina, they will wrap up their season at home Saturday against the Devils.
"We're playing our best hockey we've played all year," Callahan said. "Now is the time to do that. We've been playing playoff-style hockey the last couple of games. These are must-wins for us. It gives us a dress rehearsal for the playoffs."
Callahan made it 4-0 at 5:13 of the third with a power-play goal, flipping a shot over sprawled-out goalie Martin Brodeur, who tried to poke away the puck. Brodeur heard derisive chants of "Mar-ty, Mar-ty" throughout and finished with 18 saves.
"It's difficult to take," Brodeur said of the elimination. "We've competed real hard all year."
Lundqvist was solid in his 12th straight start, allowing only Andrei Loktionov's goal with 6:30 remaining. The Rangers had more space between games recently. The extra rest has helped Lundqvist stay sharp.
He told coach John Tortorella he won't ever ask out of the lineup.
"It's like the playoffs have been going on for a couple of weeks," Lundqvist said. "It's fun to be out there. I don't want to sit on the bench."
The Devils won't get a chance to defend their conference title. New Jersey had won two straight -- including 6-2 on Saturday against Florida -- following a 10-game skid (0-6-4).
"We pride ourselves on being there every year," forward Stephen Gionta said. "Unfortunately, we're not. It definitely hurts. The organization prides itself on winning and being in the playoffs every year. Anything less is a disappointment."
Madison Square Garden fans serenaded the Devils with chants of "Season's over" as time ticked down in the third.
"It hasn't sunk in," said Devils coach Pete DeBoer, who was ejected in the closing seconds for unsportsmanlike conduct. "You don't want to think about it until it's actually a reality. No other word but disappointment."
The Devils had already been called for two unsportsmanlike conduct penalties, one that cost them a power-play goal, before DeBoer was ushered out.
"A little frustration on my part," he said. "Two of our players were given unsportsmanlike conducts in an elimination game. The sensitivity of some of the officials is beyond me."
With a 3-0 lead heading into the third period, the Rangers had all but sealed New Jersey's fate. New York is 85-0-6 when leading after two periods, dating to Feb. 4, 2010.
The Rangers came out quickly, seemingly motivated to put the Devils away early. New Jersey knocked out New York in last year's conference finals.
New York connected right away, scoring while Brodeur was looking the opposite way from where the puck was. Carl Hagelin worked to get free from defenders behind the net, and flung the puck in front to Callahan, who was near the left post.
While Brodeur had his head turned away from him, trying to find the puck he thought was behind the net, Callahan nudged it forward off of Brodeur's skate and into the net for his 13th goal.
"They were waiting for us. We played yesterday," Brodeur said. "They were able to score the first goal, and that made a big difference in the momentum."
Pyatt played in his 800th NHL game. ... Rangers C Brian Boyle missed his third straight game because of a right leg injury. ... Volchenkov returned after serving a four-game suspension for elbowing.
Copyright by STATS LLC and The Associated Press
NEW YORK, NY - APRIL 21: Brad Richards #19 of the New York Rangers skates with the puck against the New Jersey...