Carolina, which was the No. 1 seed from the Metropolitan, lost for the first time at home this postseason (7-1).
Antti Raanta made 16 saves before sustaining a lower-body injury late in the second period. He was replaced by Pyotr Kochetkov, who made nine saves.
"We were right there with these guys," Hurricanes captain Jordan Staal said. "Anything can happen in Game 7, and obviously we're on the wrong side this time. Did we want to get to Game 7? No. We had to find a way to sneak one (win) on the road, which we didn't. Tonight was just some bounces, and everyone wasn't quite there, including myself, and unfortunately we ended the season."
Fox gave New York a 1-0 lead at 3:40 of the first period, taking a drop pass from
Alexis Lafreniere
and scoring glove side from the top of the right circle on the power play.
"Our power play has come through for us all year, and these types of games you want it to, and it did," Fox said.
Kreider scored another power-play goal to push it to 2-0 at 8:00 when he redirected Zibanejad's one-timer just above the crease.
"It was the same story. I thought we had a great first period," Carolina coach Rod Brind'Amour said. "They got the two power-play goals, and it was a killer because I really felt we were playing well. So that's kind of the broken record on this one, this series."
Shersterkin preserved the two-goal lead when he stopped a one-timer from Teuvo Teravainen with the toe of his left pad six seconds after Kreider scored on the power play.
"We scored two quick goals, and this helped me so much," Shesterkin said. "I felt a little shaky before the game, but when I go to the ice, I tried to forget about everything and tried to keep focused on the puck."