NEW YORK -- Shane Prince and Brock Nelson each had a goal and an assist, and Thomas Greiss made 33 saves to help the New York Islanders to a 5-1 win against the Toronto Maple Leafs at Barclays Center on Sunday.
Casey Cizikas, Josh Bailey and Travis Hamonic scored for the Islanders (4-5-0), who had three unanswered goals in the third period and avoided a three-game losing streak.
Greiss was asked after the game if more efforts like Sunday could one day help him become the No. 1 goalie for the Islanders. He is one of three goaltenders on New York's roster, along with Jaroslav Halak and Jean-Francois Berube.
"For sure," Greiss said. "A goalie can make a big difference in the game and you have to help your team as much as you can if you want the No. 1 spot. You have to show that you can win games for the team."
Jake Gardiner scored and Jhonas Enroth made 30 saves for the Maple Leafs (2-4-3).
"We gave up way too much to expect to win," Maple Leafs center Tyler Bozak said. "It's pretty early in the season, but there are no excuses. We weren't good enough, especially our line (with James van Riemsdyk and Mitchell Marner). [Enroth] made some really good saves, but we didn't do much for him."
Prince took advantage of a mistake by Enroth to score his second of the season 5:08 into the third for a 3-1 lead. Enroth went behind his net to corral a dump-in, but mishandled the puck and allowed Prince to steal it in the right circle and score over Enroth's blocker.
Nelson scored 2:39 later when his quick wrist shot from the slot off a feed from Prince to make it 4-1.
Video: TOR@NYI: Seidenberg, Prince help set up Nelson
Bailey scored with 44 seconds left in the third.
Islanders left wing Nikolay Kulemin, who returned to the lineup after missing the past two games because of an upper-body injury, and defenseman Dennis Seidenberg, each had two assists.
Hamonic scored his second of the season off a slap shot from the top of the right circle to give the Islanders a 1-0 lead 1:01 into the game.
"For most teams that make the Stanley Cup Playoffs, the defense is a big part of the offense, so we're trying to integrate that more and it's working out so far," Greiss said.
Cizikas made it 2-0 when he scored his first of the season off a rebound at 7:22. Cal Clutterbuck skated into the zone on 2-on-1 with Cizikas before taking a shot that deflected off Enroth to Cizikas at the left circle.
Gardiner scored a power-play goal 50 seconds into the third to make it 2-1. Gardiner scored his first of the season off a slap shot from the point with van Riemsdyk providing a screen.
Goal of the game
Prince intercepted an attempted pass by Enroth and put a shot over the goalie's blocker into the top left corner from the right circle to give the Islanders a 3-1 lead 5:08 into the third period.
Video: TOR@NYI: Prince takes advantage, pads Isles' lead
Save of the game
During a Toronto power play 13:32 into the first period, Greiss made a sensational blocker save against Maple Leafs defenseman Connor Carrick to keep the Islanders in front 2-0.
Video: TOR@NYI: Greiss slides over for blocker save
Highlight of the game
With the Islanders holding a 2-0 lead, Maple Leafs center Tyler Bozak just missed on a backhand at the left post 1:28 into the second when his attempt skittered behind Greiss, through the crease and just beyond the right post.
Unsung moment of the game
Enroth, making his second start of the season, stopped Islanders captain John Tavares on a breakaway 7:27 into the second period.
Video: TOR@NYI: Enroth stones Tavares on a breakaway
They said it
"We created a lot of opportunities, but their goalie stood on his head and made a lot of good saves. But I think we have to continue to do what we're doing and clean up some things defensively. Offensively we're getting our chances, but [we've] just got to capitalize on them now." -- Maple Leafs forward Auston Matthews
"We got the result we wanted and there were some good things, but obviously some errors we can still fix. Sometimes when you get a couple days off, it takes you a little bit to get going again. We have to be better with the puck and with coming out of our end. That's when we're a hard team to play against." -- Islanders captain John Tavares
Need to know
Maple Leafs forward Matt Martin, who spent six seasons with the Islanders before joining Toronto as a free agent, had one shot and four hits in 9:40. There was a video tribute for him during the first period. … Tavares won four of five faceoffs against Matthews, who tied for the Maple Leafs lead with four shots on goal in 18:11. … The goal by Hamonic was the ninth scored by an Islanders defenseman this season.
Video: TOR@NYI: Islanders pay tribute to Matt Martin
Maple Leafs: Home against the Edmonton Oilers on Tuesday (7:30 p.m. ET; TSN4, SNOL, NHL.TV)
Islanders: Home against the Tampa Bay Lightning on Tuesday (7:30 p.m. ET; NBCSN, NHL.TV)
Video: Islanders score early and often in 5-1 win over Leafs