NHL

GOMEZ FACTOR THE DIFFERENCE

THIS was the one free-agent defection that stung the Devils more than any other, the one that struck in their craws all season long, the one that prompted obvious resentment on the ice in the Battle of the Hudson that ended in rout last night.

Bobby Holik came to the Rangers in 2002, Scott Niedermayer left to play with his brother in 2005, Brian Rafalski left to go home to Michigan and the Red Wings this summer. The Devils understood. They even understood when Claude Lemieux forced his way out by contesting the validity of his contract after capturing the Conn Smythe Trophy in leading the team to the 1995 Stanley Cup championship.

But they didn’t understand why Scott Gomez left New Jersey to sign with the Rangers. They didn’t accept his decision as business as usual. They resented it. They felt betrayed. One Devil called Gomez, “a sellout,” during this series that the Rangers clinched with their Game 5, 5-3 victory in Newark.

Gomez got the money, sure he did, $51.5M for seven years, but he would have gotten the money other places, too. Gomez left New Jersey because he wanted more responsibility. He left New Jersey because, after seven seasons, he’d grown weary of being pulled off the ice whenever an opposing first line came on against him. He wanted to get more minutes, not more money.

Let’s put it this way. Gomez believed he had outgrown the only franchise he had ever known. He peered across the Hudson and saw not streets of gold, but greener grass.

This year and in this series, the Rangers had Gomez and the Devils did not. Two years ago, when the Devils swept the first-round Battle of the Hudson, Gomez recorded six points. This series, Gomez recorded seven points.

The numbers only begin to tell the story. When the Rangers were pinned, as they were for shifts at a time last night and in the series, Gomez invariably was able to skate it out. Gomez was able to gain the zone. Meanwhile, the Devils lacked the ingredient they’d owned since Gomez’s 1999-2000 rookie season.

“I don’t focus much on other players, but my impression of him was that he was a really great skater, and I was glad we got him,” said Ranger goalie Henrik Lundqvist. “Spending the year with him, I can say that he is a big-time player; he’s definitely one of our leaders.

“When you’re a leader, you have to step up in the big games. He did that.”

Gomez stepped up, starting the series with bruised ribs, finishing the series by scoring the goal in front that gave his team a 3-1 lead. He did it with boos ringing in his ears every time he touched the puck in Newark.

“I have to tell you, that is not easy to play against your former team; I hate it,” said Jaromir Jagr. “The booing, the bad energy, it takes something out of you. It affects you, even if you say it doesn’t.

“For Scotty to play the way he did, I’m very, very proud of him.”

Gomez of course had nothing but kind words to say about his former team. He laughed off the booing. He also laughed off a question about him being a “finisher,” as in a goal-scorer.

“I’ve never been a finisher,” he said, chuckling.

He finished off the Devils, that’s for sure; he did it on July 1 and again last night.

larry.brooks@nypost.com