Lee Stempniak scored late in the second period to snap a tie, and the Devils ended a three-game losing streak with a 5-2 win over the short-handed Rangers on Tuesday night.
"It's a big win," Stempniak said. "You can see where we are in the standings. Losing three games, it's tough to keep pace with teams. To not get points in three straight, you are going to fall behind."
The win moved the Devils within a point of Pittsburgh for the eighth and final playoff spot in the Eastern Conference. The Penguins have three games in hand with seven weeks left in the season.
"It's a critical win," said Cory Schneider, who made 17 saves. "They are all important at this time of year. You can't put a value on it but getting it against our rival after a three-game slide, it feels good."
Kyle Palmieri, Sergey Kalinin, Adam Larsson and Tyler Kennedy also scored for the Devils. Rookie Joseph Blandisi assisted on the tying and go-ahead goals in the second period as New Jersey beat the Rangers for the third time in four games this season.
"You could tell they were hungry," Lundqvist said. "This was obviously a very important game for them. The same for us. We could have distanced ourselves from them a little bit but we didn't grab that opportunity."
The Rangers played without defensemen Ryan McDonagh and Marc Staal and forward Rick Nash. They also played the third period without J.T. Miller, who received a match penalty late in the second for fighting against Kalinin with his hand taped.
The Rangers, who did not get a power play in the game, killed off 6:59 of Devils power play time in the third period with Miller's major and a tripping call against Derick Brassard.
Still, they nearly tied the game early in the period, only to see Schneider stop Moore in close on a short-handed rush.
Kalinin put the game away with 2:44 to play on a breakaway goal, his sixth of the season, and Larsson added an empty-netter in the final minute.
The Devils turned the game in the second period, taking a season-high 17 shots and limiting the Rangers to five.
"It could have been our worst period of the year," Rangers coach Alain Vigneault said. "Not to take anything away from Jersey but after what I believe was a real solid period where we had some real good looks, it was mistake after mistake in the second period. If it wasn't for Hank, it wouldn't have been a game at all."
Lundqvist kept New York in front for the first half of the period before Palmieri tied it on a power play.
Schneider made a phenomenal stick save on Miller less than a minute later, and Stempniak scored with 1:54 left for a 3-2 lead.
Blandisi, who mixed it up twice with Rangers defenseman Dylan McIlrath, had the primary assist on both Devils goals in the period. Blandisi found Palmieri alone in front at 10:28 and Stempniak in the left circle for the lead.
After falling behind early on Kennedy's second goal of the season, the Rangers took a 2-1 lead when Hayes and Moore scored in a 45-second span.
Hayes, who has four goals in seven games, tied it 1-all at 8:17, putting the rebound of Viktor Stalberg's shot into an open net. Stalberg skated the puck up the right side, cut to the middle and unleased a hard shot that Schneider could not control.
Moore put New York ahead at 9:02 with Keith Yandle making a great play to set it up. The defenseman took a pass from Marek Hrivik at the left point and sent a long pass to Moore at the side of the net. He tipped the puck past Schneider, who appeared to be waiting for a shot.
Kennedy, who didn't score in his first 30 games this season, got his second in four games 4:47 after the opening faceoff. Kalinin won the puck behind the net and sent it to Damon Severson for a point shot that Kennedy deflected.
Moore has scored five of his six goals on the road this season. ... Yandle's assist was his 30th of the season, making him the fifth Rangers defenseman to reach that total since 2001-02. ... The Devils scratched defensemen Eric Gelinas and Seth Helgeson and forward Bobby Farnham. ... Hrivik's assist was his first in the NHL. ... The win was Schneider's 26th, a career high. ... The Rangers' 19 shots matched their season low.