NEW YORK — When Alexandar Georgiev was young, his family moved from Bulgaria to Russia so he could have a better opportunity to play sports. He was happy his parents were in attendance Wednesday night to see his first NHL shutout.

Georgiev stopped 29 shots, Filip Chytil scored for the fifth straight game, and the New York Rangers beat the crosstown-rival Islanders 5-0.

"They did everything they could to help me along the way, so I'm very thankful for them," the 22-year-old Georgiev said. "It's a special moment that they were here to see my first shutout."

Chris Kreider had a goal and an assist, and Cody McLeod, Neal Pionk and Kevin Hayes also scored to help the Rangers win for the ninth time in 11 games (9-1-1). Kevin Shattenkirk and Mika Zibanejad each added two assists in the Rangers' seventh straight win at home, now by a combined 26-10 margin.

Georgiev, 7-6-1 in 15 career games coming in, made several nice stops, including 13 saves in the third period while winning his fourth straight start.

The Rangers ended an eight-game skid (0-7-1) to the Islanders, who had won 12 of the previous 13 meetings, including a 7-5 win at home last Thursday night. The shutout was the Rangers' first in the series since a 1-0 overtime win at the Nassau Coliseum on April 13, 2013.

"When you lose so often to someone you're going to win one eventually," Rangers first-year coach David Quinn said. "I think the odds were just in our favor. ... That's a really good hockey team. We were opportunistic tonight for sure."

Robin Lehner finished with 22 saves for the Islanders, who trailed 3-0 a little more than eight minutes into the game and lost for the fifth time in their last seven games (2-4-1). They also lost to a Metropolitan Division opponent for the first time after starting the season 7-0-0.

"They got out early and we were chasing all night," the Islanders' Mathew Barzal said. "We just have to have a better start. We had a lot of Grade A chances, their goalie made some big saves."

Kreider beat Lehner from the left circle on a rush with 3:41 left for his team-leading 12th to cap the scoring.

Neither team could muster anything for most of the second period until Hayes added to the Rangers' advantage, beating Lehner in front with a backhand for his fifth with 2:43 left.

Both teams finished with five shots on goal in the middle period. The Islanders had seven shots go wide, and the Rangers had one.

Chytil extended his streak and got the Rangers started in the opening minute of the game. On a 2-on-1 rush with Kreider, he was skating up the right side and tried to send a pass across the front of the goal to his teammate, but the puck deflected off Islanders defenseman Ryan Pulock back to Chytil and he beat Lehner 29 seconds in.

"When you're hot, you're hot," Hayes said of the 19-year-old Chytil. He's been playing well. ... It's impressive. It's a tough league to score goals in and he's doing it at will right now."

McLeod doubled the lead at 3:30 as he deflected Tony DeAngelo's long shot from the right point out of the air with his stick past Lehner.

The Rangers also led 2-0 less than six minutes in last week in Brooklyn before the Islanders tied it with two goals late in the opening period and went on to another win. There was no comeback this time.

"They've had our number, no doubt," Shattenkirk said. "That's huge for us as a confidence-builder going forward and just getting over that hump."

Pionk made it 3-0 on the power play at 8:04, firing a one-timer from center point that beat a screened Lehner on the blocker side for his fourth. It gave Pionk five points (one goal, four assists) in his last five games.

NOTES: Islanders F Matt Martin missed his eighth straight game due to an upper-body injury. ... Barzal ended a five-game points streak, in which he had a goal and five assists. ... The teams meet again twice — Jan. 10 at Madison Square Garden, and Jan. 12 in Brooklyn's Barclays Center. ... D Brady Skjei was back in the Rangers' lineup after sitting out the previous two games. D Brendan Smith was a healthy scratch to make room. ... Rangers F Mats Zuccarello missed his third straight game due to a groin injury. ... Rangers F Ryan Strome had an assist on McLeod's goal, giving him his first point in three games since being acquired from Edmonton last Friday. ... The Rangers have scored at least one power-play goal in five of the last six games.

UP NEXT

Islanders: At New Jersey on Friday in the second of three games in four days.

Rangers: At Philadelphia on Friday in the second of three games in four days, all against division opponents.