Joonas Korpisalo made 27 saves in his return for the Blue Jackets (28-26-3), who went 0-for-5 on the power play and lost their fourth in a row (0-2-2). Korpisalo had not played since Jan. 31 because of a lower-body injury.
"We haven't played that way in a long time," Columbus defenseman Zach Werenski said. "We've been playing hard as of late. Tonight, we let it slip and kind of handed that game to them."
Brock Nelson scored at 10:32 of the first period during a two-man advantage to give New York a 1-0 lead. Nelson took a pass from Josh Bailey, spun around Werenski and roofed a wrist shot over Korpisalo to extend his goal streak to three games.
Sorokin made nine saves in the first, including a breakaway against Boone Jenner at 9:37 during an Islanders power play.
"Usually when you get those saves or you get those breaks, you're able to turn it into something successful, and we were," Islanders coach Barry Trotz said. "We made the most of it."
Bailey made it 2-0 at 6:08 of the second period after a pass from Kyle Palmieri for his first goal in 19 games.
"It felt good," Bailey said. "You go through stretches like this throughout the course of your career, you just stick with it. There's only way through it; you can't get around it, you've just got to keep working."
Lee gave New York a 3-0 lead at 13:49 with a one-timer in the left face-off circle, and Pageau made it 4-0 at 17:44 with a shorthanded goal.
Lee scored his second of the game to make it 5-0 at 11:57 of the third period, then completed the hat trick with two seconds remaining for the 6-0 final.
"I think everybody on the ice was trying to find him," Pageau said. "Everyone was happy for him. He's been outstanding for us. The way he leads the team, day in, day out and the way he comes in and work every day, whatever the result is, you know you're going to get his 110 percent. You just want him to finish it and get the trick."