WASHINGTON — Christmas came early for the Rangers Tuesday night.

Playing their last game before the NHL’s three-day Christmas break, the team that has had so much trouble scoring goals this season found itself down a goal after two periods, but erupted for five in the third to post a stunning, come-from-behind 7-3 victory over the Washington Capitals, a team that had previously been 16-0-0 when leading after 40 minutes.

“Yeah, that was a big win,’’ said Rangers forward Alexis Lafreniere, whose 100th career goal, at 9:18 of the third period, ended up being the game-winner. “Down after two, and we come back and play a really big third like that. It’s really good for us right before the break.’’

Taylor Raddysh, who played for the Capitals last season before signing with the Rangers as a free agent over the summer, had two goals, as did Vincent Trocheck, who scored both of his in the third period. Will Cuylle (on the power play) and Artemi Panarin (into an empty net for his 200th goal as a Ranger) had the other two.

Goalie Igor Shesterkin made 29 saves, including 13 in the second period to keep the Rangers in the game. Capitals goalie Logan Thompson stopped 14 of 20 shots.

“I was happy for the players,’’ coach Mike Sullivan said. “They’ve worked so hard to try to generate more offense. It’s nice to see the puck go in the net for them. I thought the first period was a fairly even period; I thought they outplayed us in the second period. Shesty made some big saves for us, and I thought we responded really well in the third obviously.’’

The Rangers (19-16-4) enter the break having won three of their last four. They are off until Saturday when they play the Islanders at UBS Arena. They should have top defenseman and Jericho native Adam Fox back for that one. Fox, currently on long-term injured reserve with an upper-body injury, has missed the last 12 games.

On Tuesday, they were without Fox and captain J.T. Miller, who is on injured reserve with an upper-body injury. They did, however, get forwards Gabe Perreault and Matt Rempe back after they missed Sunday’s 2-1 loss in Nashville with the illness that is making its way around the locker room. Assistant coach David Quinn missed Tuesday’s game with the bug, the team said.

Raddysh opened the scoring in a sleepy first period, when he banged in a cross-ice pass from Brodzinski on a 3-on-2 rush at 14:57. It was Raddysh’s sixth goal of the season, but his first since Oct. 30 at Edmonton.

“It’s always in the back of your mind, you want to contribute as much as you can, whether it’s offensively, or defensively,’’ Raddysh said. “And for me, it’s obviously been a few games [23] since I scored my last one, so [it was nice] to get one there, right before the break, just to kind of relax and get ready to go for the second half.’’

Washington tied it 23 seconds into the second period, on a goal by defenseman John Carlson. Then, on a power play, Dylan Strome gave the Caps a 2-1 lead at 8:40, on a goal that needed video replay to confirm it happened.

Strome, standing outside the right goalpost, one-timed a cross-ice pass from Connor McMichael, but Shesterkin slid over and reached out with his glove and snatched the shot. Strome hung his head as if he’d been beaten by the save, but the Situation Room in Toronto took a look at the play and determined that the puck had definitively crossed the goal line while in Shesterkin’s glove.

“We couldn’t really tell from our angle on the bench, but obviously the referees, they have different angles and maybe a clearer television to be able to look,’’ Sullivan said. “And it was their conclusion that Shesty’s glove was [behind] the goal line.’’

Cuylle, who had three points, scored a tap-in off a shot/pass by Mika Zibanejad to tie it 2-2 at 11:14. But Aliaksei Protas banged in a rebound 57 seconds later to put Washington back in front, 3-2.

Raddysh’s second goal tied it again at 8:10 of the third, and Lafreniere’s tip-in of a long shot by Panarin put the Rangers back in the lead, 4-3, at 9:18. The Rangers ran up the score after that.

Trocheck scored his first at 13:43 for an insurance goal. Panarin scored an empty-netter at 17:44 to make it 6-3, then Trocheck scored again at 18:09 with Thompson back in the net.

Notes & quotes: Panarin’s two points gave him 588 with the Rangers, and moved him ahead of Steve Vickers (586) into ninth place in franchise history. Panarin is the second fastest player to score 200 goals (in 468 games) with the Rangers. Bill Cook did it in 363 games from 1926 to 1935 . . . The Rangers lead the league in road wins with 14. They are 14-6-1 on the road . . . D Carson Soucy skated in his 400th career game. He is in his seventh NHL season . . . Perreault (goal, two assists) has a point in three straight games.

Colin Stephenson

Colin Stephenson covers the Rangers for Newsday. He has spent more than two decades covering the NHL and just about every sports team in the New York metropolitan area.