Barzal, who also had three assists, scored with a one-timer from the left face-off circle off a return pass from Noah Dobson.
“Just a heck of an effort by the entire group tonight,” Barzal said. “It feels great to get the win. If you ask anybody around the League, this is probably the hardest place to come in and play. When they get rolling around and the crowd gets into it, it’s borderline impossible to change the momentum.”
Sebastian Aho tied it 4-4 for Carolina with three seconds left in the third period, stuffing the puck between the pads of Semyon Varlamov.
“When they tied the game, that was an awful feeling,” Varlamov said. “Three seconds left, it’s tough to give up those kinds of goals. Then ‘Barzy’ scored, it was over and we got two points. That was a crazy game. It’s the best feeling when the boys score in overtime.”
Dobson had three assists, and Varlamov made 39 saves for the Islanders (9-7-6), who are 4-1-3 in their past eight games.
“I think the whole game, we were committed,” New York coach Lane Lambert said. “We blocked a lot of shots (30), we did a lot of things we needed to do to win a hockey game in this building. I thought we did a pretty good job of making sure that we stuck to battling and not worrying about their shot total.”