The Hurricanes fell behind 2-0 but rallied to produce at least a point for the sixth straight game (4-0-2). Tuomo Ruutu picked up three assists and Justin Peters made 32 saves to get the win in his sixth start of the season.
Skinner, an 18-year-old rookie, scored the only two goals of the second period to tie the game and run his total for the season to 13.
Eric Staal put Carolina in front midway through the third and Cole then scored his ninth and 10th of the season 2:10 apart to break open the contest. His second goal was an empty-netter that came with 50 seconds remaining.
Marty Reasoner tacked on a goal for the Panthers 12 seconds later.
Tomas Vokoun stopped 30 shots in the Panthers' second straight loss.