NEW YORK -- For perhaps the first time this season, the New York Islanders had no trouble Sunday night either beginning or finishing a game.

Travis Hamonic scored 61 seconds after the opening faceoff Sunday night to give the Islanders a lead they would never relinquish in a 5-1 win over the Toronto Maple Leafs at Barclays Center.

Casey Cizikas doubled the lead at the 7:22 mark of the first period for the Islanders, who had not scored in the first period in their previous three games. New York has scored just six first-period goals this season, its fewest in any period.

"I don't think you ever know how a games going to start or end," Islanders head coach Jack Capuano said. "But you just want to play with a pace. And tonight I thought we played with some pace. We stayed in attack mode even when (the Maple Leafs) made a push."

Goalie Thomas Greiss made 23 of his 33 saves in the 32-minute span following Cizikas' goal before Jake Gardiner finally scored for the Maple Leafs 50 seconds into the third period.

But Shane Prince and Brock Nelson responded with goals during a three-minute span prior to the midway point of the third period for the Islanders, who were outscored 5-2 in the third period in losing their previous two games to the Montreal Canadiens and Pittsburgh Penguins.

"There's some games this year we've played well and come out on the losing end (on) a couple tough late goals," Islanders right winger Cal Clutterbuck said. "Sometimes those things just come back the other way if you keep working at it. That was one of those nights tonight."

Josh Bailey's even-strength goal with 43.4 seconds remaining capped the scoring and allowed the Islanders -- who have scored more goals in the third period and overtime (14) than any other period -- to end the game like they started it.

"It's good when you can score on the first and the last shift, certainly," Hamonic said with a grin. "That was a good effort. I think (the Maple Leafs) came pretty hard there in the middle of the second period, but we stuck with it."

With the win, the Islanders (4-5-0) jumped from last in the Metropolitan Division to sixth. The losing October is the first since the 2013-14 season for New York, which rode winning Octobers (6-2-3 last season, 6-4-0 in 2014-15) to playoff berths each of the last two seasons.

"Points are just as crucial now as they are in April," Hamonic said. "You need to be aware of that, and certainly we are. You want to try and collect as many early on, because it becomes so close at the end of the season. Handfuls of points can dictate a division title or missing the playoffs."

Goalie Jhonas Enroth notched 30 saves for the Maple Leafs (2-4-3), who have lost two straight and six of seven (1-4-2).

"We got the game to 2-1, we were in really good position," Maple Leafs head coach Mike Babcock said. "Then they got the third one and it seemed to break us."

The Maple Leafs have scored three goals or fewer in each of the last four games, but Babcock said he was more worried about his club's defensive play. Toronto has given up 35 goals and has surrendered at least five goals in five games.

"It's not about goal scoring, it's about the goals you give up," Babcock said. "Everyone's worried about the goal scoring. That's not our issue on this team. It's what we give up."

NOTES: The Islanders scratched C Matthew Barzal, G Jean-Francois Berube and RW Alan Quine. ... Islanders G Jaroslav Halak backed up Thomas Greiss on Sunday, one day after Halak's agent, Allan Walsh, tweeted his displeasure with the Islanders keeping three goalies active and Halak getting only one "quality practice" prior to Thursday's loss against the Pittsburgh Penguins. SNY reported Sunday that Halak asked for a trade last spring. ... The Maple Leafs scratched D Matt Hunwick (lower body), D Frank Corrando and C Peter Holland. ... Maple Leafs RW Matt Martin, who played his first seven seasons with the Islanders before signing with Toronto in July, received a standing ovation during a video tribute that aired following a first-period timeout. "It's more weird seeing him without any hair than in another uniform," Islanders right winger Cal Clutterbuck said with a grin, referring to how Martin cut his shoulder-length hair to comply with Toronto general manager Lou Lamoriello's grooming policy.