GLENDALE, Ariz. -- The Arizona Coyotes felt like they deserved a better fate in the latter stages of their nine-game losing streak. It took nearly 60 minutes for the fates to agree Saturday against the New York Islanders, but a steady diet of hard work finally paid off for Arizona.

Brendan Perlini scored the game-tying goal with 5:55 remaining and Anthony Duclair and Radim Vrbata scored in the shootout as Arizona ended a season-high losing streak one game short of the franchise record with a 2-1 victory over the Islanders.

Arizona hadn't won since Dec. 15 in Toronto.

"There were some tough games and tough mistakes but the main thing was the guys tried to learn from every game," said Perlini, who has four goals in 15 games since his call-up from Tucson of the American Hockey League. "We tried to get better at something whether we were winning or losing and I felt like the last couple games it started to show."

The Islanders lost back-to-back overtime games after winning four of their previous five games. Alan Quine scored for New York, which got 24 saves from Thomas Greiss. Greiss has allowed two goals or fewer in six of his last seven starts and has stopped 59 of 63 shots since the Islanders waived erstwhile starter Jaroslav Halak on New Year's Day and assigned him to Bridgeport of the American Hockey League, officially handing Greiss the starting job he had all but claimed with his play this season.

"We've just got to find a way to score some goals for him," New York coach Jack Capuano said. "The overtime for us tonight was probably the best overtime all year and we still can't win a game."

Coyotes backup Louis Domingue made 27 saves, including six in overtime to win for the first time since Nov. 8 against Colorado. Coyotes coach Dave Tippett criticized Domingue's performance in a loss to Calgary on New Year's Eve in which he allowed four goals on 24 shots.

"I'm not going to lie, it was a game I needed to prove something to everybody in the room, including myself," Domingue said. "It feels good."

New York finally broke out on top when Domingue made the curious decision to play the puck up the middle of the ice after stopping it behind the net. His pass missed center Laurent Dauphin and ended up on the stick of Islanders defenseman Johnny Boychuk. Quine redirected Boychuk's shot from the point into an open net for a 1-0 lead at 15:35 of the second period.

The Islanders had a chance to widen the lead late in the period with a 5-on-3 power play for 30 seconds, but Arizona had the better chances, including a 2-on-1 on which Lawson Crouse hit the post.

"It's tough to swallow when you need the points and just can't come up with it," Islanders forward Andrew Ladd said. "You've got to find ways to create offense and I felt like a lot of that tonight was just where we put the puck."

Greiss, who was the Coyotes' backup in the 2013-14 season, was sharp most of the way. He got some help from the iron when Coyotes left winger Tobias Rieder hit the crossbar on a shorthanded breakaway with just over seven minutes to play, but Arizona finally tied it when Perlini redirected Connor Murphy's shot from the point between Greiss's pads.

Duclair beat Greiss with a terrific move to his backhand in the shootout and Vrbata scored his 44th career shootout goal -- the most in NHL history -- to ice the game.

NOTES: Coyotes coach Dave Tippett joined a growing number of NHL coaches who are not fans of the league-mandated five-day break. "I think it condenses the schedule too much," Tippett said. "We come out of it and we have five games in eight days. I'm not sure what the concept is but it's not safety." ... The Coyotes recalled C Laurent Dauphin from Tucson of the American Hockey League on Saturday and he was in the lineup in place of C Martin Hanzal (lower body). Hanzal and LW Jordan Martinook (upper body) are day to day. ... With the Islanders coming off a five-day break, New York coach Jack Capuano elected to start G Thomas Greiss in both games of the back-to-back set this weekend in Colorado and Arizona. ... Islanders C Mikhail Grabovski (concussion) is on the injured non-roster list. ... Coyotes C Brad Richardson (broken right tibia and fibula) and LW Max Domi (hand) are out indefinitely. RW Ryan White (lower body) is on injured reserve.