Beauvillier, who had one goal in 16 games this season, got his first career hat trick and first four-point game. The Islanders, second in the Metropolitan Division, won for the seventh time in 10 games and remained perfect in seven games against division teams this season.

“It’s always tough mentally,” he said of his struggles. “If you don’t play good and the team’s losing it’s harder, but the team’s been winning and the locker room is great.”

Leo Komarov had a goal and an assist, and Anders Lee, Brock Nelson and Cal Clutterbuck also scored as the Islanders beat the Rangers for the 12th time in 13 meetings since the start of 2015-16 season. Valtteri Filppula had three assists, Nick Leddy added two, and Thomas Greiss stopped 36 shots.

Chris Kreider had two goals and Fredrik Claesson and Filip Chytil also scored for the Rangers, who were 6-0-1 in their last seven. Henrik Lundqvist gave up five goals on 17 shots through the first two periods. Alexandar Georgiev replaced him to start the third and had five saves.

“They had three tap-ins when they were standing next to a guy,” Rangers coach David Quinn said. “We didn’t pick sticks up. … They scored way too easily.”

Komarov scored midway through the third to give the Islanders a 6-3 lead after trailing 2-0 less than six minutes into the game.

Kreider’s second power-play goal of the night with 6:47 left pulled the Rangers back within two, and Chytil scored with 2 1/2 minutes remaining to make it 6-5.

The Rangers pulled Georgiev for an extra skater with a little more than two minutes remaining but couldn’t get the equalizer. Clutterbuck sealed the win with an empty-netter with 21 seconds left.

“These division games are huge,” Lee said. “Anytime we can get two and keep them to zero is huge.”

Beauvillier put the Islanders ahead 3-2 with his second of the night when he skated in on a breakaway and beat Lundqvist at 2:24 of the second period.

However, the Rangers tied it with a short-handed goal 57 seconds later as Hayes beat Greiss from the left circle with his fourth. It was the first short-handed goal allowed by the Islanders this season.

Beauvillier put the Islanders back ahead for good when he deflected Johnny Boychuk’s shot past Lundqvist on a power play at 5:13.

The Islanders, 2 for 24 on the power play in their previous six games, got their second of the night with the man advantage. Lee deflected Leddy’s point shot down past Lundqvist for his sixth with just under six minutes left in the middle period to push the lead to 5-3.

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