Matt Martin, Zach Parise and Brock Nelson scored for the Islanders (16-10-0), who had lost two straight.
Arvid Soderblom made 37 saves for the Blackhawks (7-13-4), who have lost nine of 10 (1-8-1).
"He made some great reads and some big saves and stood tall right to the end," Chicago coach Luke Richardson said of Soderblom. "He's been great in every appearance that he's been in. We've just got to give him a little more goal support and a little better structure in front of him."
Martin put New York ahead 1-0 at 8:58 of the second, scoring on a rebound off a shot from Casey Cizikas while battling with Filip Roos.
However, despite raising his hands while on the ice, play continued for 1:58 before a stoppage allowed the officials to review the sequence, which determined that the puck completely crossed the goal line after hitting Soderblom's pad.
It was the first even-strength goal the Islanders had scored in 175:37.
"I was laying on my back and I thought it was in," Martin said. "I was pretty confident it was in. Where the ref was, he was on the side of the net, so he probably couldn't tell. Play was going on, came to the bench, told the coaches it was in. They're like, 'Yeah, yeah.' But they looked at it and then they were confident it was in as well."