Khudobin, who served as a backup to the Boston Bruins' Tuukka Rask last season, made 9-of-10 stops during the decisive second period, during which Dvorak snapped a 1-1 tie with his second goal of the season.
Jay Harrison also scored and Jeff Skinner assisted on both Carolina tallies as Hurricanes notched their first win of 2013-14 in their second game.
Luke Schenn netted the only goal for the Flyers, who fell to 0-3 starting the season.
Steve Mason turned aside 32-of-34 shots for Philadelphia.
Notable deaths of 2014 [PHOTOS]