Seth Jarvis scored, and Frederik Andersen made 24 saves for the Hurricanes (6-5-0), who had a three-game winning streak end. They went on the penalty kill five times, including three in the first period.
"Taking five penalties is not the way to win," Carolina defenseman Brady Skjei said. "Trying to stay out of the box in the future is huge, especially against a team like this. We didn't quite have it tonight."
New York lost defenseman Adam Fox (lower body) and forward Filip Chytil (upper body) to injury. Fox's last shift ended with 5:37 left in the first. Chytil's last shift ended with 6:34 remaining in the second.
Rangers coach Peter Laviolette said both players will be evaluated Friday.
"'Fil' and 'Foxy' are really important players for us, so hopefully everything will be good," Shesterkin said. "We just tried to play our game. Cuylle stepped up in the big moment."
Kreider gave the Rangers a 1-0 lead at 2:41, scoring in front off a pass from Panarin out of the right corner. Panarin has 16 points (five goals, 11 assists) during his streak.
The Rangers were 1-for-5 on the power play but 0-for-3 without Fox, who was replaced on the top unit by Erik Gustafsson.
"Guys are going to have to step up," Trouba said. "If he's out any period of time, he's obviously a huge player in this League, a huge player for our team. It'll be on guys to step up."
Jarvis tied it 1-1 with his fourth power-play goal at 9:53 of the first after Sebastian Aho found him cutting up the middle. Jarvis got behind Trouba and Ryan Lindgren and beat Shesterkin with a high forehanded shot to the glove side.
"The first period was no good because we were in the box," Hurricanes coach Rod Brind'Amour said. "We were lucky to come out of that 1-1. Our power play made a nice play to tie the game. That's all we had that period because we were in the box."
The Hurricanes had the puck more in the second period and finished with a 9-4 advantage in shots on goal, leading to Laviolette telling the Rangers in the second intermission that they needed "more bite in their game."