This is why they need him out there.

This is why, bad back and all, the Devils need Ilya Kovalchuk for a chance to do something special in these playoffs — and after this stirring 4-3 overtime victory over the Flyers in Game 3, it’s starting to look like they could be on their way, doesn’t it?

Because there aren’t many players who could see what Kovalchuk saw, and fewer still with the skill to do something with that vision. He was several feet behind the Devils blue line, a spot where most players chip the puck up the ice and try to establish the offensive zone, especially 17½ minutes into extra time.

Kovalchuk is not most players. He saw five tired Flyers heading for the bench for a line change. He saw linemate Alexei Ponikarovsky take a couple of strides onto the ice himself.

He had a second to make a decision, maybe two. He made a pass from near the top of the Stanley Cup painted on the Prudential Center ice that hit Ponikarovsky in stride.

“He creates a situation where people don’t really have a good look at it, because he cradles the puck in his stick and he’s almost going away from the play,” said goalie Martin Brodeur, who had a better view of the play than anyone. “He’s got that great vision.

“From what I saw, he saw Poni come off the bench maybe two seconds before, and after that he never looked at him. Kovy just turned around and fired the pass right onto his stick. That’s the type of skill that he has. It’s fun to watch.”

Ponikarovsky, not the most brilliant offensive player on the team, had enough room to skate in untouched on Flyers goalie Ilya Bryzgalov. He took one shot, then picked up his own rebound and took another.

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The puck got behind Bryzgalov and The Rock erupted. For the first time since 2003, the Devils have won three consecutive games on their home ice, and most people in the building tonight know what happened then.

They are a long, long way from that. But after dropping Game 1, they’ve scored eight goals in the last four periods to take a 2-1 series lead. And after wondering how they’d survive without their $100 million star for the short term, he returned to make the difference they were counting on.

Kovalchuk was a complete nonfactor in Game 1, barely able to skate with a herniated disc in his back — an injury he said happened early in the first round series against Florida. He was scratched from Game 2, too nervous to watch the entire game on television.

“It was a difficult decision,” Kovalchuk said. “I was in my house with my wife and a couple friends. I was so nervous. I went back to put my kids to bed and then (Adam) Larsson scores” to put the Devils ahead.

“I didn’t watch a lot of hockey after that, and then my wife told me that we won. It was good.”

The Devils won 4-1, their most complete game in the playoffs, and you wondered how they’d respond with Kovalchuk back in the lineup. Every player had to elevate their game in his absence. Would they fall back into relying on him to do so much — too much — when he returned?

Turns out, the question was a moot point. The Devils scored twice in a 20-second span in the first period and Kovalchuk was involved on both goals, assisting when Patrik Elias scored on the power play and beating Flyers goalie Ilya Bryzgalov on a three-on-two rush.

The Devils would have that same one-goal lead in the third period, but you knew this night wouldn’t be easy. Another sloppy play, a defensive breakdown by the rookie Larsson and a dropped puck by Brodeur, allowed Danny Briere to tie it, and for the fourth time in five games, the Devils faced overtime.

If Kovalchuk was tired, he didn’t show it. He helped the team kill off a pair of penalties — although it was his teammate Zach Parise who generated more offense than the Flyers did on both of them — before making the pass that changed the game.

Kovalchuk is known mostly as a goal-scorer — he tallied the 400th of his career this season, and he’s just 29. But he also has 379 assists, and it’s hard to believe he’s had one as important as this, or as pretty.

“I just wanted to be myself,” he said when asked what he expected from himself as he returned to the lineup. And he was when it mattered.

The Devils don’t know what they’ll get from their injured star in the next game on Sunday, but with one brilliant pass across the ice, he showed why they need him to do something special this spring.

Steve Politi: spoliti@starledger.com; twitter.com/StevePoliti