The Hurricanes, who went into the game with the second-worst record in the Eastern Conference, have lost five in a row.
Derek Joslin brought the Hurricanes within one with 2:13 to go in the second, but Martin Biron shut down Carolina in the final stanza.
Michael Sauer gave the Rangers some insurance early in the third with his first of the season. Sauer had not played since Oct. 8 due to a shoulder injury.
Biron made 28 saves in New York's 11th win in 13 games. Cam Ward gave up all five goals on 27 shots.
Swim Week Miami Beach 2014 [PHOTOS]