"I think with our playoff runs the last couple of years, I think once you develop just that winning mentality, I feel like you can really do anything," Barzal said. "We've rattled off 13-, 14-game [point] streaks before, so I think this group's going to fight until we're in or we're out.
"We've got fans at home to entertain and put on a good show, and I think we've always been a pretty good road team, so you never know, right?"
Pius Suter and Sam Gagner scored for the Red Wings (26-31-7), who have lost eight of 10 (2-7-1). Thomas Greiss allowed three goals on 16 shots before being replaced at the start of the third period because of an upper-body injury. Alex Nedeljkovic made eight saves.
It was Greiss' first game against the Islanders since he signed a two-year contract with the Red Wings on Oct. 10, 2020. He played five seasons for New York.
"We didn't start well and we didn't have enough offensive zone time until the second and third period," Detroit captain Dylan Larkin said. "A team that likes to play at home like these guys do, you have to have a better start."
Beauvillier scored nine seconds into the game to make it 1-0, converting a one-timer from in front after Lee stole the puck from Filip Hronek.
It was the second-fastest goal to start a game in Islanders history; Bryan Trottier scored five seconds in against the Boston Bruins on March 22, 1984.
"We got a little bit of a break," Lee said. "I was able to just poke it, and 'Beau' finished it really well. It did happen quick. I don't know, we just set out to have a good start and kind of got a break to do it."
Oliver Wahlstrom made it 2-0 at 16:07 after Barzal stopped in the left face-off circle, spun and fed him for a wrist shot.
Sorokin made 13 saves in the first, including four during a 5-on-3 power play for Detroit late in the period.
"I thought [Zdeno Chara] was really important in that; he covered a lot of space with that stick and that body," New York coach Barry Trotz said. "To me, it was a tipping point. They get back in that game if they score one or two, or they put the kids to bed after that."