NEW YORK - It was a bounce three games in the making for the New Jersey Devils.

Done in by a rare misplay by Martin Brodeur in the series opener against the New York Rangers and then another odd goal in Game 2, the Devils found themselves on the brink of a short playoff stay.

A feed in front and an ill-located skate gave New Jersey new life.

John Madden scored 6:01 into overtime for the Devils, who knocked off the Rangers 4-3 on Sunday night — cutting New York’s series lead to 2-1.

Madden lost a faceoff to the right of goalie Henrik Lundqvist, but got to the loose puck in the corner. His centering pass clipped the right skate of rookie defenseman Marc Staal and caromed in.

“I’m not going to lie. It was a lot of luck,” Madden said. “I thought Sergei (Brylin) might be there, but their guy was standing there. It hit him in the foot and went in. It was real lucky, but we need to get those breaks to get back into the series.”

New Jersey beat the Rangers for just the second time in 11 games this season, and will look to tie the series in Game 4 on Wednesday night. The Devils dominated the extra period, outshooting New York 5-1, and snapped a franchise-worst, five-game playoff losing streak.

“In the overtime, we weren’t thinking. We were just going,” said forward Zach Parise, who lost two teeth in Game 2 and had root canal Saturday. “We wanted to get this win.”

New Jersey never had the lead in dropping the first two games of the series at home, but held it three times Sunday and beat the Rangers for only the second time in 11 games.

The Devils have come back from a 2-0 deficit to win once. The Rangers have blown only one such lead. Only two teams have erased an 0-3 hole and won.

“We kept battling. We kept clawing,” Madden said. “We knew there was no tomorrow if we didn’t win this game.”

Brylin made it 1-0 in the first, and Patrik Elias and Parise scored power-play goals 2:23 apart in the second.

Rangers rookie Brandon Dubinsky scored his first two career playoff goals, getting New York even at 1 and 3. Sean Avery scored for the third straight game, a 5-on-3 tally in the second period, and continued to be a pest to Brodeur. Jaromir Jagr had three assists.

It just wasn’t enough.

“Those first two games, the lucky breaks went our way. Today it went their way in overtime,” Jagr said. “Nobody said it was going to be easy. It’s going to be hard. We have to take the positive. We’re still ahead 2-1.

“Next game, we have to win it. That’s the bottom line.”

Brodeur shook off a blow to the head late in regulation, finishing with 27 saves and earning his 95th playoff victory. He has started 156 consecutive postseason games for the Devils.

Lundqvist, who hadn’t allowed more than two goals in 10 previous games against New Jersey this season, stopped 29 shots.

New Jersey nearly ended it even sooner when Brian Gionta rattled a shot off the right post 2 minutes into overtime. Elias also struck a post a few seconds later.

The low-scoring series that was anticipated took shape in the opening two games, but it took until Game 3 for overtime to become necessary. Four of the eight regular-season meetings between the cross-river rivals also required extra time — all but last Sunday’s season finale were won by the Rangers.

“This time around we got the bounces,” Brodeur said. “The last two times at home, they went the Rangers’ way. This was a confidence booster for us and a lesson in how to play these guys.”

The Rangers again did damage in the third period, forging the third tie of the night 55 seconds in on Dubinsky’s second goal during a power play. New York has outscored the Devils in the third 6-1 in the series and 13-2 this season.

Brodeur held tough the rest of the period and absorbed a hit to the head from Ryan Callahan, who crashed into him with 2:36 left in regulation. Stunned and dazed, Brodeur worked out his jaw and put his helmet back on after briefly being attended to by a trainer.

The Devils grabbed their first series lead 3:01 in and had to sweat out a lengthy video review before their third goal in three games became official.

Dubinsky tied it at 1 with 7:43 left in the first, and the Rangers put their power play to work in the second.

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Just 10 seconds after Vitaly Vishnevski went off for elbowing Avery, fellow defenseman Bryce Salvador joined him in the box for knocking a puck into the seats.

Avery continued to annoy Brodeur, who smacked the Rangers forward in frustration as he was hounded and face-guarded. When Scott Gomez spotted Avery in front, he sent a perfect feed from the goal line to Brodeur’s left for a redirection score 6:50 into the second.

“It’s a 5-on-3 and I’m trying to get to the puck,” Brodeur said. “I’m trying to look around him. It was almost impossible because of the stick so close to my face. I’ve played for 15 years in this league; I’ve been watching games for 33 years. I had never seen that in my life.

“I don’t think that kind of behavior should be done in front of the net, but there is no rule for it.”

Payback was New Jersey’s as the Rangers gave the Devils three power plays within a 3:47 span of the second. Elias and Parise cashed in two to make it 3-2 with 3:41 left in the second.

Notes: Vishnevski returned to the Devils lineup after being scratched the first two games of the series. D Andy Greene sat out. ... The Devils dropped the final three games of last year’s second-round series against Ottawa. ... The Rangers had won six straight first-round games, starting with a sweep of Atlanta last year.