The penalty kill came up big and Jaroslav Halak made 36 saves as the New York Islanders downed the New York Rangers 4-2 at Barclays Center Tuesday night. The win gave the Islanders at least a point in each of their last five games (4-0-1).

“It’s gives our guys confidence that they can play with some of the top teams in the East,” Islanders head coach Jack Capuano said. “I think it was a good game. I think our goalie, early on during the first two power plays, was the determining factor. He was dialed in tonight.”

The Islanders got a key contribution early from defenseman Scott Mayfield who was called up from Bridgeport earlier on Tuesday on an emergency basis when Johnny Boychuk fell ill with flu-like symptoms. Mayfield’s blast from the top of the circle gave the Islanders a 1-0 lead at 7:03.

“It just goes back to the fact that you have to be ready at all times,” Mayfield said. “I’m getting kind of used to it. Now I kind of know what I need to do when I get here and how I need to play.”

The rest of the period belonged to the Islanders penalty killers and Halak in particular. The veteran goalie made several huge saves after Brock Nelson was sent for for a 4:00 high sticking penalty to keep the score 1-0 for the home team. The Rangers did everything but score on the lengthy power play and Halak stepped up and became the team’s best penalty killer.

The goalie also had help from his teammates who blocked several shots on the penalty kill and a total of 28 shots in the game, led by Calvin de Haan (seven) and Travis Hamonic (six).

“It was a good effort by our PK, blocking so many shots,” Halak said. “A few times they made saves for me and kept it out. It’s always nice to see the guys making saves around you when you’re not there.”

The Islanders then cashed in just after the power play expired when Nelson came out of the penalty box and fed Jason Chimera just outside the crease. Chimera put the puck past Henrik Lundqvist at 17:24 and the Islanders led 2-0.

The Isles maintained that lead as the teams headed into the dressing room for the first intermission despite being outshot 16-9.

The Rangers got back into the game just 56 seconds into the middle stanza when Jimmy Vesey put home a second rebound to cut the Isles lead to 2-1.

The Islanders responded quickly and regained a two-goal lead when Shane Prince’s aggressive forecheck forced a turnover and Andrew Ladd scored just 1:22 after the Vesey goal to make the score 3-1 Islanders.

The Rangers scored the prettiest goal of the night midway through the second period when Marc Staal cashed in after a series of perfect cross-ice passes to pull the Rangers back to within 3-2.

The Islanders did not let up in the third period and continued to play strong defense. The power play clicked at 11:13 when John Tavares ripped home a one-timer past Lundqvist to give the Isles a 4-2 advantage.

The Rangers had a pair of power-play chances late in the game but the Islanders penalty killers came up big again and preserved the 4-2 win. The Islanders killed off all six Rangers chances with the extra attacker and have not allowed a goal on their last 18 penalty kills stretching back seven games.

The Islanders are no longer alone in the Eastern Conference cellar and continue to gain confidence with their recent strong play which includes victories over strong rivals like the Capitals, Penguins and Rangers.

“No secret if you want to be a good team, you’ve got to beat some of the top teams in the league,” captain John Tavares said. “Certainly being able to do that has been big for us. We feel like we deserved to get those wins. I think we recognize there’s some good building blocks going.”

The Islanders return to action Thursday night when they host the St. Louis Blues at the Barclays Center.

NOTES:

Official attendance was 15,795

By assisting on Tavares’ power play goal, Bailey extended his point scoring streak to six games.

The Rangers lost Rick Nash in the second period to a lower-body injury while Matt Puempel left the game with an apparent concussion early on.

In addition to Boychuk, the Islanders scratched Anthony Beauvillier and Thomas Greiss. J.F. Berube served as the backup goalie.

Jaroslav Halak is now 9-1-0 in his last 10 games against Henrik Lundqvist.