Stepan, scoreless on the season coming into contest, recorded his second career hat trick for the Rangers, who picked up a third straight win and ninth in a row over the Hurricanes.
Mats Zuccarello and Chris Kreider each helped out three assists and Henrik Lundqvist made 27 saves.
Andrej Sekera collected the only goal for slumping Carolina, which dropped a fifth straight game.
Justin Peters recorded 33 saves.
Celebrity Families of 2014 [PHOTOS]