With their season pretty much hanging on the result, the Devils got down and dirty. With a chance to put a stranglehold on this series, the Rangers lost their grip.

There will be no payback sweep for the Rangers now - John Madden’s good-fortune goal guaranteed that. When it pinballed home off the skate of Rangers defenseman Marc Staal 6:01 into overtime, it lifted the Devils to a 4-3 victory in Game 3 of the teams’ crackling Eastern Conference quarterfinal.

With the opportunity to take a 3-0 lead in the series after two victories in Newark, the Rangers rallied to tie in the third period but never threatened in a Devils-controlled overtime. And after an icing, though Brandon Dubinsky won a faceoff from Madden, Devils winger Jay Pandolfo darted in to tie up Rangers defenseman Michal Rozsival, freeing the puck.

Madden was first to it and he threw it in front from a sharp angle. It wasn’t headed on goal until it struck Staal’s right skate and ricocheted through the pads of Rangers goaltender Henrik Lundqvist.

It was the third Devils goal of the night that bounced past Lundqvist off a teammate. Lundqvist had allowed three goals to the Devils only once in his last 17 regular-season and playoff games against them.

“As far as bounces, hey, we got the bounces the first two games,” Rangers center Scott Gomez said. “Don’t take anything away from them. They had their backs to the wall and they got themselves back in the series. Now, we’ve got to respond. You make your own bounces at this time of year.”

The Devils did so with a desperate effort appropriate to their dire situation. The Rangers matched the Devils’ intensity and physicality in the most rollicking game of the series. But the Rangers’ discipline wasn’t up to the level of the first two games.

In fact, after Sean Avery’s 5-on-3 goal 6:50 into the second period - shortly after the Ranger agitator spent a few moments face-guarding Brodeur, with his back to the puck and his hands and stick in the Devil goaltender’s face - gave them a 2-1 lead, the Rangers appeared to get caught up in the moment. They committed three straight minor penalties over the period’s final 12:45. And the Devils made them pay by scoring twice on a power play that went 1-for-27 against the Rangers during the regular season but has three goals in this series.

Zach Parise’s go-ahead goal came off a sharp-angle shot that struck a sliding Brendan Shanahan’s stick and wound up bouncing over Lundqvist, who was down on his side, giving the Devils a 3-2 lead. But the Rangers erased it just 55 seconds into the third when Dubinsky, who played a commanding game, converted a Jaromir Jagr rebound on a power play. It was the second goal of the night for Dubinsky - the 21-year-old center scored his first career playoff goal in the first period to tie the game at 1-1 - and the third assist for Jagr.

Despite chances galore at both ends the rest of the third period - and a goalmouth collision with Ryan Callahan that knocked Martin Brodeur’s helmet and mask off - the series’ first overtime followed. And with it came the notion that the next goal would either all but finish off the Devils or give them life.

It did the latter. Whether it also put a dent in the Rangers’ psyches after a lengthy run of big-moment success against the Devils was a question put to Tom Renney.

“I guess time will tell,” the Rangers’ coach said. “We didn’t expect this to be a walk in the park. It’s a seven-game series. They’re a good team. We’ve had close games with them all year long. The puck bounces as it does. And tonight it was their turn.

“I don’t think we’re going to dwell on this to the point where we’re completely deflated. We’re not. This happens.”

Shanahan was similarly philosophical, stating that the Rangers’ wealth of experienced and accomplished veterans must be tapped under such circumstances.

“I don’t think that anybody either way predicted sweep for the Devils or sweep for the Rangers,” Shanahan said. “So I don’t think that anybody in here feels like the series got away or anything like that. It was a tight game and a strange bounce.

“It’s not a devastating thing. We just come back to work and try to get the next game.”