WASHINGTON — The kids are more than all right. And now they’ll get to see if can carry it over into the playoffs.

It wasn’t pretty, it wasn’t easy, but it sure was unexpected. Keyed by goalie Christopher Gibson, making his first NHL start against the most potent team in the league, the injury-riddled Islanders pulled out a comeback overtime victory against the Capitals, 4-3, Tuesday night at Verizon Center.

With the win, the Islanders clinched at least a wild-card berth. What’s more, they did it on the second day of a back-to-back, without two of their top defenseman, and two rookies starting in their place.

Thomas Hickey scored on a feed from John Tavares 2:13 into overtime and Gibson made three straight impressive saves in the first minutes of the OT — including one on a breakaway by Evgeny Kuznetsov — to erase third-period lapses that temporarily put the Isles in a two-goal hole.

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“I don’t have any words to say,” said Gibson, essentially the Isles’ fourth-string goalie. “I’m still on a high from that game . . . The guy [Kuznetsov] was coming down and in my mind, I was like, ‘I have to stop this to keep this going.’ Lucky enough, I made the save there and we won the game. I believed in our team and I knew we were going to come back.”

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T.J. Oshie and Ovechkin scored back-to-back goals in the opening seven minutes of the third period to give the Capitals a 3-1 lead. But Kyle Okposo and Anders Lee brought the Islanders right back. Okposo scored at 8:40 — off a bounce on Tavares’ saved shot — and Lee tied it at 3 less than two minutes later, on a deflection of Nick Leddy’s shot.

Ovechkin scored twice, giving him 47 points in 41 career games against the Isles, but using somewhat of a makeshift lineup, the Islanders managed to creep up on the President’s Trophy-winning Capitals.

Playing with fellow rookies Ryan Pulock and Scott Mayfield on defense, and without Travis Hamonic (lower body) and Calvin de Haan (game-time decision), Gibson made 29 saves. That included a head’s-up stop on Marcus Johansson’s 2-on-1 attempt to keep the Capitals’ lead at 1-0 early in the second period. At 13:43 of the second, Tavares scored on a one-timer from Hickey to tie it at one.

A Capitals win would have tied Braden Holtby with Martin Brodeur’s single-season record of 48. Instead, Holtby got undone by an upstart. Gibson was an emergency recall from Bridgeport Monday after an injury to backup J-F Berube (day to day) and had played only one other NHL game: a relief effort against the Penguins on Jan. 2.

“It’s special,” Tavares said. “He saved my rear end when I turned it over there at the line (in overtime) . . . That’s a great feeling he’ll remember.”

The Islanders were two points away from clinching before the game, and though the Bruins eventually lost, which would have secured the Islanders a spot anyway, Boston took the Hurricanes to overtime.

“I think (we did it) the hard way,” Hickey said. “We didn’t wait for someone else to do it for us. To come here at the back end of a back-to-back and have someone like Gibby and play through a little adversity there, that’s the right way to do it. You’d rather do it the hard way than the easy way.”