ANAHEIM, Calif. -- The New York Islanders had to survive their opponents' late rally, a barrage of shots in overtime and the longest shootout in team history to earn a rare victory.

Nick Leddy scored in the 14th shootout round to give the Islanders a 3-2 win over the Anaheim Ducks on Tuesday night at the Honda Center.

Adam Pelech and Josh Bailey scored in regulation for the Islanders (6-8-4), who broke a four-game losing streak with just their second victory this month and their first on the road this season.

"We needed this so bad," Islanders defenseman Thomas Hickey said. "We need the two points (Wednesday), too, and the two points after that."

The Islanders will continue their three-game road trip in Los Angeles against the Kings on Wednesday night, then end it with Friday against the San Jose Sharks.

New York goalie Thomas Greiss stopped a season-high 39 shots, including seven in overtime, for his first victory since Oct. 23. He was beaten four times on Anaheim's 14 shootout attempts. Greiss made his last start Nov. 1.

"He's such a calm presence back there, even in a shootout," Hickey said. "It's funny watching him play sometimes. He's an old-school, standup goalie. He's just comfortable back there, and it rubs off on everyone else."

Cam Fowler and Rickard Rakell scored for the Ducks (9-7-4), who used the shootout point they received to move into first place in the Pacific Division by one point over the Kings and the Edmonton Oilers. Goalie Jonathan Bernier made 33 saves before he was beaten five times in the shootout.

"Every time we scored, they found a way to score," Bernier said about the shootout. "I take this loss on my shoulders. A couple of times, I was overreacting before they even made a move."

Two rounds before Leddy scored, New York needed a goal to prevent Anaheim from winning. Shea Theodore converted a backhand over Greiss's right shoulder to put the Ducks in position to win. Hickey had to score to keep the shootout going.

Bernier appeared to block Hickey's backhand with his left leg pad while prone on the ice. As Bernier dragged his leg backward, officials ruled that the puck crossed the goal line, though the leg pad still covered the puck.

"I made the save," Bernier said. "My skate was going right to the post, where I wanted it to be and (Hickey) pushed me in."

After a long video review, Hickey's goal was allowed to stand.

"The explanation I was given was that they called it a goal on the ice, so they couldn't determine that the puck wasn't in the net under his pad," Anaheim coach Randy Carlyle said. "It was inconclusive. They couldn't tell if the puck was in the net or not."

Rakell tied the score at 9:08 of the third period when he received Corey Perry's pass from the right circle and converted a wrist shot from the left circle for his third goal in the past three games. The 23-year-old Swede has seven goals and 11 points in 11 games since signing a six-year contract extension Oct. 14.

Both goalies made crucial saves in the final two minutes of regulation. After stopping a slap shot from New York's Travis Harmonic, Bernier reached backward to prevent Brock Nelson from poking the rebound inside the right post with 1:42 left. With 1:15 and 1:05 remaining, Greiss used his blocker to stop rising shots from Ryan Kesler and Perry, respectively.

The Islanders took a 2-1 lead in the first period after Fowler's power-play goal put the Ducks ahead 1:04 into the game. Fowler fired a slap shot from the left point inside the right post for his sixth goal 26 seconds after New York's Anthony Beauvillier received a hooking penalty.

Pelech's first goal of the season, a slap shot from the blue line, tied the score at 11:51. Then with 3:18 left in the period, Bailey scored his third goal when he one-timed a shot that ricocheted off the right post from the right circle during a power play.

Anaheim defenseman Sami Vatanen left the game in the first period with the flu. Vatanen's availability for the Friday game against the Chicago Blackhawks is uncertain, Carlyle said.

NOTES: New York scratched D Scott Mayfield, C Shane Prince and G Jaroslav Halak, the Islanders' first-string goalie who started the previous seven games. ... Islanders LW Nikolay Kulemin played his 600th career game. ... The Islanders lead the NHL with 361 blocked shots. ... Anaheim scratched LW Joseph Cramarossa, D Korbinian Holzer and D Clayton Stoner. ... Ducks C Antoine Vermette set a team record Sunday night by winning 95.2 percent of his faceoffs (20 of 21) against the Los Angeles Kings. Vermette compiled the fourth-best percentage in history (minimum 20 faceoffs) since the NHL began tabulating faceoff statistics in 1997-98.