Semyon Varlamov had his shutout streak end at 142:10 but made 30 saves for the Islanders (3-1-0), who were 2-for-3 on the power play. Noah Dobson had two assists.
The teams play again at Prudential Center on Sunday (7 p.m. ET; MSG+, MSG+ 2, NHL.TV).
"We only had one [goal] the last two, so we wanted to get back to it," Islanders center Brock Nelson said. "We have confidence in everybody in the room. … As much as everybody would like for the team to score six every night, that's not how it works, so we've just got to find ways to win."
Nathan Bastian scored, and Scott Wedgewood started and made 31 saves for the Devils (2-1-1) after goalie Mackenzie Blackwood was placed on the NHL list of players unavailable to play or practice in accordance with COVID-19 protocols Thursday. It was Wedgewood's first start since Feb. 13, 2018, when he made 28 saves for the Arizona Coyotes in a 2-1 win at the San Jose Sharks.
"I was told this morning at pregame skate, and then I obviously feel for [Blackwood] kind of getting that call," Wedgewood said. "His health is important, so taking the right precautions is good for him. On my end I was excited. It's been a long time since I got in the net at the NHL level, over three years I think it's been, so I was excited to see what I can do and help the guys win."
Barzal gave the Islanders a 1-0 lead at 4:43 of the first period when he carried the puck from the neutral zone and scored with a wrist shot from the right circle.
"I'm always trying to grow my game," said Barzal, who has scored twice in four games. "Obviously, just the last couple of years [I've been] pass first and whatnot, but I'd still say that's still my game. One of my best attributes I think would be my passing, it always has been. But I play with 'Ebs' and [Anders Lee], who are good at creating space and giving me chances, so it was like that tonight. … I think for me, just try to be more assertive. When I do get into a chance where it's like pass or shoot, just try to bear down and let one go."