The Rangers held on for a 4-3 win on Monday night to snap a three-game losing streak, but they almost squandered a three-goal lead against a team they routinely beat.
Mats Zuccarello and Oscar Lindberg scored first-period power-play goals to get New York rolling.
Chris Kreider and Derick Brassard also had goals and New York improved to 18-1-0 in its last 19 meetings with Carolina.
Henrik Lundqvist made 33 saves.
Jordan Staal, Victor Rask and Chris Terry scored for the Hurricanes.
Rangers center Derek Stepan will miss four to six weeks because of broken ribs. New York coach Alain Vigneault made the announcement following the morning skate.