The Sabres reached 12 wins for the season, becoming the first team in the Eastern Conference to do so.
This is Enroth's third year with the Sabres, but he was appearing in only his 25th game. He ran his record this season to 7-1, having been forced into action when regular goaltender Ryan Miller suffered a concussion.
Buffalo has won seven of its last eight and Enroth bounced back from a struggling effort on Wednesday when he was pulled after giving up five goals against New Jersey.
Buffalo's goal came from Jason Pominville on the power play with 6:56 to go in the first period. It was his eighth of the year.
Brian Boucher made 19 saves for the Hurricanes, who have lost three straight and seven out of eight. They have been shut out twice in a row.