Noah Dobson, Anthony Beauvillier and Jordan Eberle also scored for New York, and rookie Ilya Sorokin stopped 16 shots. The Islanders improved to 5-0-1 in their last six overall and 8-0-2 at the Nassau Coliseum to remain the only team without a regulation loss at home.
"That's when we're at our best, when we have four lines rolling," Martin said. "We're a tough team to beat when we're playing like that. This was a good one. We just got to keep it going."
Taylor Hall and Rasmus Ristolainen scored for Buffalo, which has lost five straight (0-5-1). The Sabres are 2-8-1 since taking a two-week break for a COVID outbreak.
Jonas Johansson, making his second start of the season with starter Linus Ullmark injured, finished with a career-high 40 saves.
"It was a very bad game," Ristolainen said. "I feel like every time we were kind of getting back at it, getting the momentum in their zone, and getting some good shifts then we made a mistake. I made unfortunately a lot of mistakes today that cost us the game."
The teams continue the series with afternoon games at the Coliseum on Saturday and Sunday.
Sorokin, coming off 20-save shutouts in his previous two games, had six saves in the first period, four in the second and six in the third to improve to 3-2-1.
With Buffalo trailing 3-1, Jeff Skinner hit a goal post from the left circle in the opening minute of the third.
Eberle then put the Islanders ahead 4-1 as he scored on a rebound of a shot by Anders Lee at 3:14, beating Johansson on the glove side.
Ristolainen pulled the Sabres back within two at 7:23, jamming in the rebound of a shot by Jack Eichel for his third.
Martin got his second of the night and fourth of the season as he converted the rebound of his own shot from the right doorstep with 5:32 left. It was Martin's third career two-goal game, and first since March 25, 2014, at Carolina.
The Islanders, in the midst of a stretch of 19 games in 33 days, got their seventh straight win against the Sabres, including four this season.
"I think it's important if we're going to have success, the games where we have everybody contributing, being on the right side," Islanders coach Barry Trotz said. "We've got a very busy stretch here, we're going to have to manage it."
Hall got the Sabres on the scoreboard at 3:08 of the second. Sorokin made a save on Cody Eakin's shot from the left side, but Hall put in the rebound from the right side to make it 2-1.
Beauvillier restored the Islanders' two-goal lead on a breakaway with 5:02 left in the middle period. Beauvillier, playing in his 300th career game, got a pass from Brock Nelson, sped ahead of Ristolainen and skated in and beat Johansson for his second.
"Nelly put it in the space for me and yeah, it felt pretty good to score a goal," said the 23-year-old Beauvillier, in his fifth NHL season. "Feels like yesterday I first started playing here. I wouldn't call myself an older guy. I'm still young at heart, I guess. It's been a fun ride so far and looking forward to the rest of it."
The Islanders outshot the Sabres 18-6 while scoring twice in a dominant first period.
Dobson put the Islanders up 1-0 as he got a pass from Eberle in the middle and fired a shot past Johansson's blocker for his second with 9:25 left.
Martin doubled New York's lead on a fortuitous deflection as he sent the puck from the left corner beyond the goal line off Johansson's mask and in with 3:39 left.
"Initially I was looking to find (Casey Cizikas) or (Cal Clutterbuck) around the net," Martin said. "They weren't really open. Everyone kind of gravitated to them and I took a look at the goalie and saw he was down and just tried to put it there. Luckily I was able to hit my spot and it went in."
Trotz said Martin has been working on that shot in practice and liked that it worked.
"Well-placed shot and really timely goal for us," Trotz said.
The Islanders are outscoring opponents 26-13 in the third period this season for a league-best plus-13 margin in the period. New York has a 17-5 margin in the third at home.
Hall's goal early in the second was only his second of the season and first since Buffalo's season-opener against Washington on Jan. 14. He got the Sabres' first goal of the season in his first game with the team after signing a one-year, $8 million deal in the offseason.
THREE IN A ROW
This is the second time in franchise history the Islanders are facing the same opponent in three straight games. New York previously did it March 4-10, 2012, against New Jersey. The Islanders will do it three more times this season: March 11-14 against New Jersey, March 18-22 against Philadelphia and April 22-27 against Washington. This is the only time all the games are in the same arena.
The Sabres are playing three straight against the same team in the same season for the first time.
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