The Rangers celebrate an empty-net goal by left wing Jimmy...

The Rangers celebrate an empty-net goal by left wing Jimmy Vesey in the third period of an NHL game against the Capitals at Madison Square Garden on Tuesday. Credit: Kathleen Malone-Van Dyke

The Rangers haven’t looked good in probably a month, since they dismantled the Carolina Hurricanes in Raleigh the night before the Super Bowl. But they are starting to see signs, they say, that remind them of what they are capable of when they play well and everything clicks.

The first period of Tuesday night’s game at Madison Square Garden against the Washington Capitals was one of those signs. The Rangers took the first 11 shots of the game, blitzing the visitors, who didn’t seem to know what hit them. And in the end, that first period was the biggest reason the Blueshirts were able to power past the Capitals, 5-3, in the opener of a five-game homestand.

“I think everyone, you can tell, is a little bit frustrated here, at the way we’ve played, so we came out hot tonight,’’ said Patrick Kane, who played his best game since becoming a Ranger two weeks ago.

Kane scored a power-play goal, and an assist, Mika Zibanejad had a pair of goals in the first period, and goaltender Igor Shesterkin had another strong performance, with 28 saves and a spectacular assist, as the Rangers won for the third time in four games, and won in regulation for the first time since Feb. 26.

“I think we know how we’re capable of playing, and just getting it all the time, consistently, is what we’re striving for,’’ said captain Jacob Trouba, whose goal at 4:09 of the second period gave the Rangers a 4-1 lead.

“I think we’re getting better,’’ he said. “I think today was — the start was better than what we had on the trip, I think. We liked our first period. Second period wasn’t our best. The third was a little bit back and forth. But I think a big key is knowing what we’re capable of doing and how we’re capable of playing.’’

Coming off a three-game road trip to Montreal, Buffalo and Pittsburgh, in which every game went to overtime and the third period was their best period in each game, the Rangers needed a fast start against the Caps and they got it. They outshot Washington 19-9 in the opening 20 minutes, and led 3-1.

“Yeah, that first period was outstanding,’’ coach Gerard Gallant said. ‘’They shot the puck, they got inside, they did a lot of real good things. So we’re real happy with the first period. And after that it was OK, but it was much better than the previous games.’’

Zibanejad’s first goal, at 4:09 of the first, gave them a 1-0 lead, but a deflection by Nicolas Aube-Kubel of a Matt Irwin shot at 14:29 of the period tied it for Washington. But Zibanejad’s second goal of the game untied it just 16 seconds later, and the goal was set up by Shesterkin.

The goalie collected the puck after a dump-in on following the faceoff and lifted it up high and deep, looking for Artemi Panarin, breaking up the left wing. Panarin got the puck in stride, and backhanded a pass to Zibanejad in the slot. Zibanejad roofed a backhand shot over Washington goalie Darcy Kuemper to make it 2-1.

Kane made it 3-1 on a power play at 18:46, when he used Washington’s Matt Irwin as a screen and blasted a slapshot through a crowd and by Kuemper for his third goal (in six games) as a Ranger. Trouba’s goal made it 4-1, and it looked like they were going to run away with it.

But the Capitals got back on the scoreboard when Irwin fired a left point shot that deflected off the leg of Rangers defenseman Niko Mikkola and got behind Shesterkin to make it 4-2 at 12:08 of the second. When Nic Dowd jammed in his own rebound to pull Washington within 4-3 at 11:48 of the third, the Rangers had to sweat a little.

But Jimmy Vesey’s backhand clearance from inside his own blue line went all the way down the ice and into the empty net to make it 5-3 with 2:11 left.

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