Rangers defenseman Adam Fox (23) celebrates with teammates after a...

Rangers defenseman Adam Fox (23) celebrates with teammates after a goal against the Washington Nationals by center Vincent Trocheck (16) during the second period in Game 3 of an NHL hockey Stanley Cup first-round playoff series, Friday, April 26, 2024, in Washington. Credit: AP/Tom Brenner

WASHINGTON — When they made their run to the Eastern Conference finals two years ago, the Rangers were absolutely exhausted when it was over, having played 20 games in 40 days, one every other day for six weeks.

They should have a chance to get some rest this time around.

Riding another big night by their specialty teams and with goalie Igor Shesterkin shrugging off an early goal against to make 28 saves, the Rangers put together a 3-1 victory over the Washington Capitals in Game 3 of their first-round playoff series Friday night at Capital One Arena, putting them on the brink of advancing to the second round. They lead 3-0 in the best-of-seven series and can close out the series with a victory in Game 4 on Sunday.

The Rangers, winners of the Presidents’ Trophy and prohibitive favorites to dispatch the wild-card Capitals, had one power-play goal in four attempts Friday night, and their penalty kill was 6-for-6 and scored a shorthanded goal. In the first three games of the series, the Rangers are 13-for-15 (86.7%) on the penalty kill. And they have scored as many shorthanded goals (two) as the Capitals have scored power-play goals.

“I think we were able to capitalize on some of the opportunities that we got at pretty important times,’’ said Chris Kreider, who scored the Rangers’ first goal and who plays on both the power play and penalty kill. “I think we probably went to the box a few too many times, but I think the penalty kill did a great job. And Shesty, especially, did a great job.’’

Vincent Trocheck had a power-play goal and an assist on Barclay Goodrow’s shorthanded goal. Mika Zibanejad had assists on Trocheck’s goal and on Kreider’s. Washington goaltender Charlie Lindgren made 19 saves.

Shesterkin, who was beaten by a long shot from John Carlson in the first period that put the Rangers in a 1-0 hole, recovered to earn the 16th playoff victory of his career, tying him with John Davidson for the fifth-highest total in team history.

Shesterkin’s best save was one in the second period in which he slid post-to-post to make a stop on a point-blank effort by Max Pacioretty. But he also had one against Hendrix Lapierre late in the second. When Lapierre found himself all alone in the slot as an errant Rangers pass came to him, Shesterkin charged out from his goal crease to give Lapierre no net to shoot at and swallowed the puck in his midsection.

“First of all, that [Carlson shot] goes off my stick, so it’s a bad bounce,’’ Zibanejad said. “Obviously, early in the game, but [Shesterkin’s] been there for us all year. We know what kind of goalie he is, but just to see him play the way he did tonight was huge for us.’’

Carlson’s goal put the Capitals up 1-0 at 5:34 of the first period, but just 34 seconds later, Kreider tipped Zibanejad’s shot past Lindgren for his second goal of the series, tying it at 1-1.

Then, with Ryan Lindgren — Charlie’s brother — in the box for a cross-checking penalty, Trocheck and Goodrow managed to break into the Capitals’ zone two-on-one against Alex Ovechkin. As Ovechkin drove over to play Trocheck, he passed to Goodrow, who beat Lindgren to put the Rangers up 2-1 at 8:08.

Trocheck’s goal at 15:22 of the second period made it 3-1. Shesterkin and the Rangers’ defense made it hold up.

Now the Rangers have the chance to sweep the series and earn a few days of rest, which Goodrow, who won two Stanley Cups with Tampa Bay, said would be key.

“Obviously that’s huge,’’ he said. “This time of year, everyone’s playing a lot, everyone’s getting banged up. So whenever you get rest, it’s for sure beneficial.’’

Notes & quotes: Kreider’s goal was his 67th career playoff point, tying him with Rod Gilbert for third-most in franchise history . . . Matt Rempe was given an interference penalty in the first period for a hit on Washington defenseman Trevor van Riemsdyk, who left the game and did not return . . . Coach Peter Laviolette was asked if he had any thoughts on how the series is being officiated, with the teams totaling 27 power plays in three games. “I do have thoughts,’’ he said. When asked if he wished to share those thoughts, he said simply, “I do not.’’

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