Eric Gelinas scored on a power play 1:15 into overtime, after the Devils squandered the lead in the final seconds of regulation, to lift New Jersey to a 4-3 win Saturday night.
The Devils managed only 11 shots Friday in a 3-1 home loss to Detroit. They fired 24 at Rangers goalie Henrik Lundqvist, and got four past the man with the new seven-year, $59.5 million contract.
"I'm fortunate to be out there in that type of situation, and I gave it a shot," Gelinas said. "It definitely feels good to be rewarded and to get that winner, but it was a team effort."
New Jersey has won all three meetings against the Rangers this season, including two at Madison Square Garden, with two remaining.
"These are fun games to play," said Devils goalie Martin Brodeur, who wore new pads without breaking them in. "To come in here, get the puck to the net, score some goals, it feels good."
"My intent was to swing around and get his stick, but it comes up too high and catches him," Callahan said. "It's a bad penalty. It cost us a point."
Brodeur made 21 saves for the Devils, who earned just their third win in nine games (3-5-1).
Brad Richards and Mats Zuccarello also had goals for the Rangers, who again failed to move two games over .500 as they began a nine-game homestand. Lundqvist made 20 saves in his first home start since signing his contract extension.
The Rangers fell to 11-1-1 when leading after two periods and 14-2-1 when scoring first.
"It's a big point," Lundqvist said of the overtime loss. "We never gave up, so that's a good sign. We just didn't get the bounces."
Zajac, in his 500th NHL game, got the Devils even when he cleaned up a rebound of a shot by Jagr and scored from in close.
The Devils, with revamped line combinations and changes to the lineup, put early pressure on Lundqvist, but despite recording the first three shots, New Jersey fell behind 3:32 in.
New York raced out of its zone on a 2-on-1 break, with Richards carrying the puck on left wing alongside Callahan to his right. Richards snapped a drive from the left circle -- the Rangers' first shot -- that beat Brodeur stick side for his team-leading ninth and second in two games.
There was more jump to the Devils' offense than on Friday, yet they couldn't get anything past Lundqvist in the first period on nine shots.
"We knew we were going to need some depth contributions," Devils coach Pete DeBoer said. "We got them from Janssen, the fourth line, Peter Harrold, who I thought was excellent.
"We needed a lot of energy, and those guys gave it to us."
The Rangers made the most of their early offense again in the second period, this time scoring on their second shot that came off a big rebound.
Callahan ripped a drive from the right circle that Brodeur sticked away to his right, but it came to Zuccarello, who stepped into a hard shot from the left circle that easily found its way into the open left side 57 seconds in.
New Jersey got a fortunate bounce when Janssen's third of the season cut the deficit in half at 6:02.
The rugged forward, who scored only three goals in 312 career NHL games before this season, crashed the net toward a rebound of Sestito's shot and knocked the puck past Lundqvist with his left skate. The on-ice call stood up to a video review.
"I thought it was a kick, but it doesn't matter," said Lundqvist, who will make his third straight start Sunday against Washington. "They got it, and in the end they just managed to get the bounces. It's a frustrating loss."
Brodeur earned the secondary assist, the 43rd of his career.
Rangers D Marc Staal was struck in the head by the arm of New Jersey's Reid Boucher in the third period and left the game. It wasn't immediately known if Staal would play Sunday. ... Harrold filled in for D Marek Zidlicky, who sat out with an upper-body injury. RW Damien Brunner returned to the lineup after being a healthy scratch Friday, replacing C Jacob Josefson. ... D Justin Falk replaced D Michael Del Zotto, and newly recalled C J.T. Miller took LW Benoit Pouliot's place in the Rangers lineup. RW Derek Dorsett sat out for the fourth time in six games with a wrist injury.