Jordan Eberle had a goal and an assist, Casey Cizikas had two assists, and Ilya Sorokin made 16 saves for the Islanders (13-6-4), who have a six-game point streak (5-0-1) and are the only NHL team without a regulation loss at home (8-0-2).
"We feel we have four lines and three sets of [defensemen] that can contribute," Eberle said. "I think if you look at the minutes across the board, most nights are fairly even. That's just (coach) Barry [Trotz] having confidence in everybody. That's what makes our team such a good hockey club; we win by committee and each guy has a role."
Taylor Hall and Rasmus Ristolainen scored for the Sabres (6-12-3), who have lost five in a row. Jonas Johansson made 40 saves.
It was the opener of a three-game set; New York will host Buffalo again Saturday.
"A lot of turnovers, not managing the puck well and that cost us the game," Ristolainen said. "I mean, everyone is trying to make plays. No one wants to [stink], no one wants to make a mistake, no one wants to be on the ice to let other team score. But, yeah, we've got to figure it out."
Noah Dobson gave the Islanders a 1-0 lead when he took a pass from Eberle and scored from the top of the right circle at 10:25 of the first period.
Martin made it 2-0 at 16:21 of the first when he banked a shot from below the goal line off Johansson's mask.
"Initially I was looking to find Casey and [Cal Clutterbuck] and they weren't really open," Martin said. "Everyone kind of gravitated to them. Then I took a look at the goalie and saw that he was down and just tried to put it there. Luckily, I was able to hit my spot and it went in."
Hall ended a 19-game goal drought when he scored on a rebound from the bottom of the right circle to cut it to 2-1 at 3:08 of the second period. It was his second goal of the season and first since the season opener on Jan. 14.
"No matter what the score is in the game, you have to defend hard," Hall said. "I feel like at times through the goal-scoring drought you tend to overthink things and you tend to worry about not scoring instead of playing an overall game that's solid and the goals will come. Tonight was a little bit better in that aspect."