The Rangers played without defenseman Ryan McDonagh, who is out with an abdominal strain.
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"Obviously, when you lose your best defensive player, it's tough to fill that hole, but I thought our guys did a really good job," said Brendan Smith, who was plus-4. "We made the simple plays and it helped us early."
Sebastian Aho scored for the Hurricanes (9-7-4), who had won two straight.
The Rangers scored on their first two shots of the game. J.T. Miller and Smith made cross-ice passes before Kreider finished a one-timer from the right circle for a 1-0 lead at 52 seconds of the first period.
"Unbelievable play by Brendan, really heads up play," Kreider said. "There were a bunch of other ones I probably should have put in too. Guys were really looking for me."
Zibanejad pushed the lead to 2-0 at 2:26 on a mistake by Hurricanes goaltender Scott Darling. Zibanejad flipped the puck on goal from inside the red line, but Darling reached across his body with his glove and fanned on the puck.