The Islanders didn’t let the All-Star break derail their good play against another good team.

A 3-2 win over the East-leading Capitals Tuesday night gave the Islanders five wins in six games under Doug Weight and three straight victories over three of the NHL’s best. The Isles pulled within three points of the Flyers for the final playoff spot and the Islanders have three games in hand on them.

There were wins over the Blue Jackets and Canadiens last week before the players scattered for a three-day break and now the Caps, who came steamrolling into the Barclays Center on a 12-1-1 tear and left with a narrow loss thanks to some more effective forecheck work by the Islanders, who snapped a 1-1 tie on just such an effort by rookie Anthony Beauvillier behind the Washington net to start a play that Ryan Strome finished.

“We just beat Columbus and Montreal so we’ve got no reason to feel down about ourselves going into the third (tied),” said Strome, who finished off a good feed from Brock Nelson for his first goal since Dec. 31. “We’re playing poised and confident and we’re getting results.”

After controlling the second period and allowing just five Capitals shots while tying the game on Alan Quine’s power-play goal, the Isles felt some pushback from the Caps at the start of the third.

Thomas Greiss, the ink just dry on his three-year, $10-million extension, made a few key stops early in the third to keep it tied among the 15 he had in the final period. And on a rare foray deep into the Caps zone the Isles struck.

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Beauvillier picked off a back pass along the end wall and fed Nelson, who turned and hit Strome for a pretty goal past Philipp Grubauer.

The Caps surged further but the Islanders held strong, taking a 3-1 lead on Johnny Boychuk’s empty-netter at 18:52 and holding on after Alex Ovechkin pulled the game back to within a goal at 19:13.

But this one marked the second straight game that the Islanders won when tied after two. They had been 4-6-4 prior to that, lamenting all the points they gave away late in tied games.

“I wish I knew (why it changed),” Quine said. “I think we learned how bad it felt to lose all those games at the beginning of the year. It took us longer than we wanted to realize we can’t keep doing that. It’s playoff hockey now for us.”

For Weight, the first period was sloppy — somewhat expected after the weekend layoff. A poor defense change left Evgeny Kuznetsov with loads of speed and room to beat Greiss just 4:41 into the game, which could have been seriously deflating to an Isles team that was running on all cylinders a few days ago.

“I thought we were containing too much,” Weight said. “You have to play faster in the D zone than you do in the offensive zone. We were much better at that in the second.”

And in the third, they weathered a few stormy moments to find themselves inching to the top of the list of non-playoff teams rather than being buried at the bottom as they were the first three months of the season.

“We’re in the conversation now,” Weight said. “Still a long way to go. We’re doing our battling late in games, getting the saves, getting some smart play from all four lines.”