Back at Madison Square Garden just two days after winning their second straight seven-game series, the battle-hardened Rangers drew on their reserves of stamina to win the opening game of the Eastern Conference final 3-0.
After two scoreless periods, defenseman Dan Girardi broke the stalemate less than a minute into the third then forward Chris Kreider blasted a second goal eight minutes from the end.
Russian center Artem Anisimov wrapped up the scoring by putting the puck into an empty net to give the Rangers a 1-0 lead in the best-of-seven series.
"We've been in these games all play-offs," said New York head coach John Tortorella, who called a timeout late in the second period to give his weary players a chance to catch their breath.
"I have tremendous confidence in our condition and more importantly our mental makeup.
"We still have a month to play. We're not a tired hockey club, we're ready to play."
The Devils were the fresher of the two teams after wrapping up their semi-final against the Philadelphia Flyers in five games almost a week ago but could not find a way past Rangers' goalie Henrik Lundqvist.
The Swede, one of three players shortlisted for this season's Most Valuable Player award, was an impenetrable force at the back, saving all 21 shots fired at his goal.
"We worked really hard. It's always tough to come from a Game Seven, where it's so emotional and you start all over again," said Lundqvist.
"It means a lot to the whole group that we can go out in a game like this and just raise our level in the third period."
New Jersey netminder Martin Brodeur turned away 25 shots but was helpless to stop Girardi's blast after Kreider tracked down a bouncing puck.
Revitalised by the goal, the Rangers sealed their victory when Kreider scored on a power play and Anisimov guided the puck into the empty net after Brodeur was pulled.
"We have to be better. We know that and we will," said Devils' winger Zach Parise. "We played well for 40 minutes and that was it.
"That last 20, we let it slip away a little bit and they took advantage and that's the game right there."
Game Two will be back at Madison Square Garden on Wednesday before the series moves over the Hudson River to New Jersey for two games.
The winner will advance to the Stanley Cup final against either Los Angeles Kings or Phoenix Coyotes.