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.
NOTES: 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.