NEW YORK -- Jaroslav Halak nearly let it get away twice but did just enough between the pipes to give the New York Islanders a win against a rival.

Halak allowed a bad-angle goal late in the third period that tied the game and accidentally knocked a puck into his own net during a shootout, but his 38 saves and final two stops in the shootout helped the Islanders survive in a 4-3 victory against the New York Rangers on Thursday night at Madison Square Garden.

The Islanders entered the third period with a 3-1 lead but sloppy play led to Mats Zuccarello cutting the lead in half and Kevin Hayes evening the game at with a backhander from along the goal line that squeezed between Halak and the short-side post.

Josh Bailey near won the game for the Islanders in the final seconds, but Rangers goaltender Henrik Lundqvist made two incredible saves to send the game to overtime.

After five scoreless minutes, shootout goals by John Tavares and Jordan Eberle and helped give the Islanders (3-3-1) a much-needed victory after a 1-2-0 road trip through California.

"Obviously, it was an unfortunate bounce," Halak said of Hayes' goal. "It was one of those were I tried to seal the post and somehow it went in. It looked like the puck had eyes. We didn't panic. We stayed with it. I'm happy for the shootout win, and we just need to build on it."

The Islanders also hope to build on their power-play success Thursday. They went 1-for-3 on the man advantage to break an 0-for-20 drought to open the season. Anders Lee converted on the Islanders' first power play of the game, stuffing home a rebound after Ryan Pulock's shot was deflected by a diving defender.

"We just needed a goal," Islanders coach Doug Weight said. "We did some good things prior to today, but you need to break through. It was early, it got us the lead, so it loosened the bench up a little because you start squeezing (the stick) a little bit. It was big."

Rookie forward Mathew Barzal, the Islanders' first-round pick in 2015, also broke through with his first NHL goal early in the second period to put his team ahead 3-1. He stormed down the left wing around Rangers forward Rick Nash and slipped the puck past Lundqvist, who made 35 saves and later denied Barzal a second goal with two highlight-reel stops.

"It's like, I'm happy I scored, but at the same time, I'm a little bit frustrated because I thought I could've had a couple more," Barzal said.

Barzal's frustration can't possibly match that of the Rangers (1-5-2), who are off to their worst eight-game start to a season since they were 0-14-1 out of the gate in 1943-44.

"That's the challenge we face right now as a group," Rangers coach Alain Vigneault said about the team's mentality potentially going bad. "The only way to get those bounces is to continue to play the right way and work hard."

"I really thought it was a good third period," said Nash, who has just one goal in eight games and failed to convert numerous dangerous chances Thursday. "Sooner or later, you have to convert. Goals come in bunches, and you know when you're in a drought, it's always tough."

Relinquishing a two-goal lead against a division rival is never the ideal way to earn a victory, but the Islanders will be satisfied with the two points and holding the Rangers down in the standings.

"When you're down, you push, you take chances and start throwing pucks," Weight said of the Rangers' late rally. "You get things to the net and you get a little desperate. You can't always blame your hockey club for hanging on for a win. It's tough, but we'll work at some things (Friday) and talk about some things, but it was a big win."

NOTES: Islanders D Ryan Pulock made his season debut after sitting as a healthy scratch for the team's first six games. He was a minus-1 with three shots on goal in 8:33 of ice time. Pulock took the place of LW Nikolay Kulemin, as Islanders coach Doug Weight opted to use seven defensemen and 11 forwards. ... The Islanders also scratched D Dennis Seidenberg and LW Anthony Beauvillier. ... The Rangers employed the same lineup they used Tuesday in a loss to the Pittsburgh Penguins. ... The Rangers have allowed at least one power-play goal in six of eight games this season.