The Islanders' Nick Leddy and Mathew Barzal celebrate a goal during...

The Islanders' Nick Leddy and Mathew Barzal celebrate a goal during the second period of a game against the Sabres on Monday in Buffalo N.Y. Credit: AP/Jeffrey T. Barnes

BUFFALO — The new year clearly holds plenty of promise for the Islanders. They finally appear headed in the right direction under the leadership of president and general manager Lou Lamoriello and coach Barry Trotz, with their drastically improved defensive play and, by necessity, the recent addition of top prospects Josh Ho-Sang, Michael Dal Colle and Devon Toews into their lineup.

“The fact that everyone is giving 100 percent every shift, it rewards you,” said goalie Robin Lehner, victorious as he faced the Sabres for the first time after spending the previous three seasons with them. “It gives you some karma.”

The Islanders concluded 2018 by holding on for a 3-1 win Monday night at KeyBank Center. They were outshot 13-3 in the third period and played nearly the whole game without third-line center and top penalty-killer Valtteri Filppula. But Lehner made 39 saves and Trotz earned his 783rd coaching victory, moving him into sole possession of fourth place on the NHL’s all-time list, one ahead of Islanders Hall of Famer Al Arbour.

The Islanders (21-13-4), who missed the playoffs the previous two seasons and have won only one series since 1993, have won seven of their last eight games. A season after allowing 293 goals, the most in the league since 2007, they have given up only 102, the fewest in the NHL.

“The last [season] wasn’t great the way it finished and with the departure of John [Tavares],” Trotz said. “A lot of things were said of what would be this year. Lou came in and it’s in good hands. I would say there’s light. It’s not all dark and we’re going forward.”

Carter Hutton made 30 saves for the Sabres (21-13-6), now in a 4-7-4 slump, and his first-period paddle save on Josh Bailey likely will be on some end-of-season highlight reels. But Lehner, who has allowed one or fewer goals in six of his last seven starts, was the better goalie.

“This one felt good,” said Lehner, nine months sober after battling alcohol and pill addiction as well as mental-health issues during his time with the Sabres. “It was probably the hardest game I’ve played in my career. I don’t know why. It was a really weird feeling for me. I struggled mentally a little bit in the beginning of the game.”

Lehner was greeted with a smattering of polite applause and some quiet booing when he was announced as a starter and during a quick “welcome back” video at 5:35 of the first period.

Former Islander Kyle Okposo, who snapped a career-worst 21-game goal drought, ended Lehner’s impressive shutout streak at 177:36 with a power-play goal from the right circle at 10:14 of the third period to pull the Sabres within 2-1. But Lehner got an assist on Ryan Pulock’s fluky empty-netter with 31.4 seconds left.

Lehner left the puck for Pulock behind the Isles’ net and he flipped it high off the glass in his own end, trying to get the puck out. The Sabres’ Zach Bogosian, at the right point, jumped up to try and knock it down, but the puck went off Bogosian’s glove and rolled — slowly — into the Buffalo net.

“You could tell he wanted this one badly,” Casey Cizikas said of Lehner. “He stood on his head from the opening get-go. He deserved this one.”

The short road trip opened with an emotional 4-0 win in Toronto on Saturday night as the Islanders faced Tavares for the first time. Lamoriello and forwards Leo Komarov and Matt Martin returned to Toronto for the first time since leaving the Maple Leafs.

There was no letdown Monday despite a sluggish start. Nick Leddy’s shot from the left point gave the Islanders a 1-0 lead at 2:59 of the second. Brock Nelson made it 2-0 at 1:45 of the third with a shot from the slot off Hutton’s glove.

“We’re molding to the team that Barry wants us to be,” Leddy said. “We’re really starting to understand the last couple of games that getting the puck north, making the easy play, getting pucks to the net and playing team defense is a successful way to play.”

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