Beauvillier won it on a wraparound for his fourth goal of the season.
"It's one of those instinct plays," Beauvillier said. "It just happens and then you kind of hope for the best. It's a play where you kind of go behind the net and you see the goalie isn't really there and you kind of go for it.
"I was fortunate; it kind of hit a skate and went in the net tonight. It's one of those plays where you just kind of do it and sometimes you get lucky with it."
Ilya Sorokin made an NHL career-high 36 saves for the Islanders (21-8-4) and extended his winning streak to eight games.
Oskar Lindblom scored for the Flyers (15-11-4), who lost the last two of three consecutive games against the Islanders. Brian Elliott made 17 saves.
"We played a pretty good game," Philadelphia center Sean Couturier said. "We outshot them, had our chances, but we couldn't capitalize and they get two bounces their way and they cashed in."
The Islanders were outshot 26-10 through the second period but credited Sorokin with keeping it a one-goal game.
Sorokin is the first Russia-born rookie goalie to win eight consecutive NHL games; Igor Shesterkin (New York Rangers) and Ilya Samsonov (Washington Capitals) each won seven in a row last season.
"[The Flyers] were on top of us a little bit, [but] we survived it," New York coach Barry Trotz said. " ... They were a committed group tonight, and when you run into that, you need someone to rise, and tonight Ilya did that for us. He made some real key saves at key moments, and we were able to grind our way back into an even game, and fortunately we finally beat them in overtime."