Price notched his third shutout of the season for the Habs, who next face the Bruins in Boston Thursday.
Brendan Gallagher and Max Pacioretty each provided a goal and an assist.
Brandon Prust also scored for Montreal.
Anton Khudobin made 27 saves for the Hurricanes, who fell for the first time in five games.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys