Skinner is the youngest player in the league at 18 years, 10 months. He has collected 58 points and his performance Wednesday helped keep the Hurricanes in the chase for the final playoff spot in the Eastern Conference.
Carolina is three points behind both the New York Rangers and Buffalo, who are tied for seventh place.
Skinner's two goals came in the first period, running his season total to 29. Mike Cammalleri brought Montreal within one early in the middle period but Jamie McBain and Joni Pitkanen both scored in the span of 2:57 to give the Hurricanes a 4-1 advantage heading into the third.
McBain added his second goal of the game with 4:36 to play.
The win went to Cam Ward, who made 38 saves.
Carey Price surrendered four goals on 26 shots through two periods before giving way to Alex Auld.
Montreal, which is just two points in front of the Rangers and Sabres for sixth place, has lost four out of five.