Jean-Gabriel Pageau of the Islanders fights Jacob Trouba of the Rangers...

Jean-Gabriel Pageau of the Islanders fights Jacob Trouba of the Rangers during the third period at NYCB Live's Nassau Coliseum on Tuesday. Credit: Jim McIsaac

On the first full day after the trading deadline, the Islanders and Rangers did the opposite of regrouping, taking stock and resting up for what promises to be a frenetic stretch run: They played against one another.

The result was another playoff-intensity tussle between the two old rivals that added to the point totals of both, and was another step for the surging Rangers in their improbable late-season run at a playoff spot.

It is far too soon to draw any conclusions about Monday’s deadline moves — most notably the Islanders’ trade for (and signing of) Jean-Gabriel Pageau and the Rangers’ re-signing of Chris Kreider — but we already know this:

The next few weeks are going to be mighty interesting around here.

The Rangers’ 4-3 overtime victory Tuesday night at NYCB Live’s Nassau Coliseum was their eighth in the past nine games overall and eighth in a row on the road.

And it moved them within five points of the Islanders in the wild-card playoff standings and within four of the Blue Jackets, who hold the second and final wild-card spot.

This was not what most people expected of the still-rebuilding Rangers. But here we are.

Marc Staal said he missed the intensity of meaningful late-season games the past two seasons.  “It feels good to be back in the mix,” he said.

After Brock Nelson’s goal tied it for the Islanders with 17.9 seconds left in the third period, Mika Zibanejad won it 18 seconds into overtime with a blast from the slot.

“I think we had it in us to play this way,” he said afterward. “Obviously, the consistency has been the issue.”

The drama of the playoff race drove the urgency with which the Islanders, Rangers and another Metro foe, the Hurricanes, handled Monday’s big day.

For the Islanders, that centered on Pageau, who made a big first impression.

First, he scored to make it 2-1 when he poked in the rebound of a Ryan Pulock blast that caromed off the boards.

Then fans sang Pageau’s name to celebrate. Then, he further endeared himself to his new teammates and fans by going after Jacob Trouba after Trouba had leveled his linemate, Michael Dal Colle.

Pageau was given a two-minute, five-minute and game misconduct penalties for his trouble.

Before the game, his new teammates praised his arrival.

“The goal is to win a Stanley Cup,” Matt Martin said. “I think Lou [Lamoriello], [Barry Trotz] and the organization, not only with [Pageau] but also with [Andy Greene] put us in a better position to do so, and we’re excited.”

Derick Brassard, who grew up near Pageau and is a fellow French Canadian, said the added buzz was evident during the morning skate.

“This is probably the biggest pickup [in the league] on the trade deadline,” he said. “It sends a strong message for our dressing room. We felt like we could beat anybody with the team that we had before, but now with Greene and Pageau, we’re up there.”

As for the Rangers, the way they reacted Tuesday was another sign of their grit.

Coach David Quinn called Monday “emotional,” “awkward” and “strange,” citing the re-signing of Kreider, the trade of Brady Skjei to Carolina and the Brooklyn car accident that injured Igor Shesterkin and Pavel Buchnevich.

But he had a one-word answer about what retaining Kreider was like for him: “Christmas.”

After the game, he said, “I don’t know how many people here thought we’d be in this position we are. Nobody inside the walls of that locker room is surprised, and neither is the staff.”

Tuesday night’s game was the last this regular season between the Rangers and Islanders, but both teams separately will play many more games with postseason implications.

“For sure, I think it’s great for the area having two good teams going at it,” Martin said before the game. “Obviously, with all of the teams in the area there hasn’t been a lot of that — Knicks, Nets, Giants, Jets. I think the fans look forward to this on both sides.”

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