Oliver Wahlstrom scored two goals for the Islanders (1-2-0), who lost their previous two games on this stretch of 13 straight on the road.
Sorokin lost his shutout when MacKenzie Entwistle scored with 26 seconds remaining.
"I wanted him to get the shutout," New York coach Barry Trotz said. "He deserved the shutout, but we failed in the last few seconds. But he played really solid. He made the saves he needed to make and some that were timely."
Marc-Andre Fleury allowed three goals in the third period and finished with 25 saves for the Blackhawks, who are still seeking their first win (0-3-1).
"We probably didn't deserve to come out on top in any of the first three games, but today if a couple of those go our way early on we feel it's a different game," Chicago captain Jonathan Toews said. "We'll find that consistency as a team, we'll settle in. Every team goes through a spurt early in the year where you're going to have four, five, six games that don't go your way and nothing really feels like it's rolling downhill for you.
"It's frustrating, no doubt. But whenever you go through that, you have a choice and the only choice for us is to keep working through it and to look for solutions to get better because of it.
Sorokin made 18 saves in the first period, including two point-blank chances for Alex DeBrincat.
"He definitely bailed us out in that first period," Wahlstrom said of Sorokin. "He's a world-class goalie. It's tough to score on him in practice. It was really good for him to get that win. He played unbelievable. He bailed us out a couple of times and I'm happy for him."
Anthony Beauvillier gave New York a 1-0 lead at 4:08 of the second period when he collected a loose puck behind the net and pushed it past Fleury for an unassisted goal. It was Beauvillier's first of the season.