Drayson Bowman and Nathan Gerbe also scored for Carolina (1-3-0), while Khudobin made 41 saves.
Rookie Michael Bournival was the lone scorer for Montreal (1-2-1). Carey Price stopped 24 shots for the Canadiens.
This was Montreal's second game in two nights against the Hurricanes. The Canadiens beat Carolina 6-0 in a lopsided match in Quebec City on Friday.
This one wasn't as one-sided, but Montreal found few answers to the Carolina netminder's superb play. Khudobin, who played 14 games with Boston last year and is slated to become the Hurricanes' backup goalie this year, was impressive early and throughout the game.
The Hurricanes, who have played four pre-season games in as many nights, showed no sign of fatigue after Friday's game.
Carolina opened the scoring at the end of the first period when Bowman fired home his first goal of the pre-season into a gaping net.
Price misplayed a clearance behind his net, leaving the puck for Eric Staal, who passed it to a wide-open Bowman.
Skinner added to the Hurricanes' lead early in the second period, taking a pass from Riley Nash and firing home on a 2-on-1. The goal would prove to be the winner.
Carolina put the contest out of reach at the end of the second period when Nathan Gerbe fired a shot past Price on the power play. It was the Habs' fourth penalty of the period.
Montreal scored a consolation goal late in the third period when Andrei Markov's shot banked off Bournival's shin. It was Bournival's fourth goal of the pre-season.