Their shock was even greater when that advantage was gone, and they were suddenly locked in a tie game in the opening minute of the third period.
In the end, it all worked out for the Devils, who got another surprising goal from fourth-line forward Ryan Carter in the closing minutes and escaped with a win that put New Jersey on the brink of a spot in the Stanley Cup finals.
Carter's third goal of the playoffs with 4:24 remaining was the difference in the Devils' 5-3 victory over New York on Wednesday night. The Devils have a 3-2 edge in the series, but if the top-seeded Rangers can stay alive on Friday night in New Jersey, Game 7 would be back in Madison Square Garden on Sunday.
''It's a good feeling,'' goalie Martin Brodeur said of the Devils' status. ''We worked really hard to get in that position. (There's been) a lot of unsung heroes and guys producing at different times. Players are playing well. We've just got to keep going.
''Nothing is done yet.''
If the Rangers fall short, their best season in years will come to a crashing end and the Devils will move on to face the Western champion Los Angeles Kings. New York hasn't been to the finals since 1994, when the Rangers knocked out New Jersey in the semis and then beat Vancouver for the title.
The Devils are one win away from playing for the Cup one season after their run of 13 straight postseason appearances was snapped. New Jersey went to the finals four times between 1995 and 2003 and won three championships.
''It's a great position to be in,'' Devils forward Patrik Elias said. ''Hopefully, we can play a better game at home. Hopefully, we'll be the team that dictates the energy and the pace out there.''
When Travis Zajac scored 9:49 in to make it 3-0, the Devils seemed ready to cruise to victory. But the Rangers roared back and appeared to have every bit of the momentum.
Then the game, and perhaps the entire series, changed in the blink of an eye when Carter put the Devils in front to stay. Zach Parise added an empty-net goal to make sure the Rangers had no chance for another comeback.
Carter had only four goals and four assists in 72 regular-season games with Florida and New Jersey. He has two goals in the East finals.
''They've been great the whole playoffs,'' Elias said of the fourth line. ''It's not always the top guys who win you hockey games.''
Stephen Gionta and Elias scored within the first 4:13 before Zajac made it 3-0. Then the Rangers woke up.
Brandon Prust brought New York within 3-1 before the first period was over, and Ryan Callahan made it a one-goal game in the first minute of the second. The Garden really rocked when Marian Gaborik tied it at 3 just 17 seconds into the third.
But the comeback was for naught.
''We probably played our best game of the series,'' Rangers coach John Tortorella said.
Once Gaborik tied it with an unassisted goal that ricocheted in off Brodeur's skate, it appeared the Rangers would ride the comeback all the way to one of the most stirring wins in team history - one that would rival victories over New Jersey in the classic 1994 East finals when the Rangers erased a 3-2 series hole behind Mark Messier's guarantee.
Carter made sure it wouldn't happen.
''You have to (keep it together) this time of year,'' Gionta said. ''You have to have a short memory. Fortunately we did and came out with the victory.''
New Jersey was outshot 28-17 overall and had only six shots in the third period, but two went in.
Brodeur, the backbone of every New Jersey title, kept his focus throughout the third when he was loudly taunted with chants of ''Mar-ty, Mar-ty'' after New York got even.
''It was a mistake,'' Brodeur said of Gaborik's goal. ''I'm pretty happy that the boys bounced back and made this a win for us. It would have been tough and people would have blamed that mishandle.''
The Rangers were ultimately done in by another terrible start. They had been on a pattern of win-one, lose-one, but now they are on the verge of elimination with their second two-game losing streak in a series this year.
The only time the Rangers have won two straight in a playoff series this postseason is when they overcame a 3-2 hole in the first round and knocked out Ottawa.
''We have to bring all the good things we did and keep doing them in the next game,'' Rangers goalie Henrik Lundqvist said. ''We played really well in the second and third period.''
They couldn't say the same about the first.
''It's different when you go down 3-0. You don't have a whole lot to lose,'' Rangers forward Brian Boyle said. ''It was good nonetheless. Now it's 3-2. Now we have to win two. That's the bottom line.''
The Rangers burned their timeout early, and Devils coach Peter DeBoer spent his with 10:17 left. Parise implored his teammates on the bench - ''Come on boys!'' - and the messages from the coach and the captain did the trick.
''It wasn't pretty by any means,'' Parise said. ''But we're going home with a 3-2 lead.''
Not only didn't the Rangers have the strong start they craved and insisted they needed, they were practically run out of their building.
The same problems that plagued New York in its 4-1 loss in Game 4, when the Devils jumped out to a 2-0 lead in the first period, cropped up again in front of the frustrated fans.
Gionta got the Devils going 2:43 in, and Elias made it 2-0 1:30 later on New Jersey's fourth shot.
Tortorella used his timeout, but it made little difference. He appeared to be calm as he moved back and forth behind the bench while talking to his players. Whatever the message was it didn't sink in.
The Devils shrugged off a few scoring chances by the Rangers, and padded their lead again.
Just 5:26 after Elias' goal, Zajac made it 3-0 with his seventh of the playoffs. Zajac got a clean shot from just inside the right circle that beat Lundqvist inside the left post.
The tide began to turn the Rangers' way, and they allowed only one shot the rest of the period.
Prust, making his return following a one-game suspension for an elbow he delivered to the head of Devils defenseman Anton Volchenkov in Game 3, showed off a bit of scoring touch when he converted on a breakaway with 4:19 left in the first to make it 3-1.
The Rangers outshot the Devils 9-6 in the lopsided period, but continued their sudden defensive dominance well into the second. Then they cut the Devils' lead to a goal just 32 seconds into the second.
New Jersey didn't record its first shot of the period, and its second since its third goal, until Adam Henrique put a puck in on Lundqvist at 6:23.
Lundqvist, who had stopped 94 percent of the shots he faced in the playoffs before Wednesday, made just 12 saves. The Rangers allowed five goals one game after giving up four for the first time in this postseason.
To make the finals, New York will have to win a third consecutive seven-game series.
''We have to have a short memory,'' Rangers defenseman Ryan McDonagh said. ''We've been in this position before in this playoffs and we found a way to get it done. We don't want to look ahead. We have to win two games, but we just have to focus on winning one.''
Notes: Brandon Dubinsky had been sidelined since he was injured in the Rangers' victory over Ottawa in Game 7 of the first round. He sat out all seven games of the second round against Washington and the first four against New Jersey. John Mitchell was scratched to make room in the lineup. Prust's return forced D Steve Eminger to sit out after he played the two previous games. ... Ilya Kovalchuk has 10 assists in the playoffs. ... Prust scored his first career NHL playoff goal in his 23rd game.