Kochetkov missed Carolina’s first 11 games with a lower-body injury. He made 22 saves in a win with the Chicago Wolves of the American Hockey League on Saturday before being recalled on Sunday.
Nikolaj Ehlers scored his first goal with the Hurricanes (8-4-0), and Sean Walker had a goal and an assist.
The Rangers (6-6-2) stretched their home winless streak to start the season to six games (0-5-1), tying a franchise record originally set in 1943-44 (0-5 with one tie) and then again in 1950-51 (0-3 with three ties). They have been shut out in four of the six games and held to one goal in another.
Igor Shesterkin made 29 saves.
Ehlers’ first goal of the season gave the Hurricanes a 1-0 lead at 13:30 of the first period.
He scored on the power play with a shot from the top of the left face-off circle through traffic, including a Seth Jarvis screen. Sebastian Aho won the face-off in the left circle back to Walker, who walked it to his right inside the blue line before passing the puck back to Ehlers.
Ehlers signed a six-year, $51 million contract with the Hurricanes on July 3.
Walker made it 2-0 at 17:07 of the second period.
The Hurricanes again scored seconds after a face-off win. Mark Jankowski won it back to Mike Reilly, who moved the puck across the blue line to Walker for a shot from above the right circle. Jankowski was screening Shesterkin and nearly got his stick on the puck for a tip-in.
Jarvis scored into the empty net to make it 3-0 at 18:21 of the third period.
The Rangers had 13 shots on goal in the first 8:40 of the game, but just two shots in the final 11:20 of the first period. They didn’t score on nine shots in the second period. They had one in the third.
They had a stretch of 21:18 without a shot on goal; the final 8:08 of the second period through the first 13:10 of the third.