Phoenix overcame a two-goal deficit to win for the third time in four games after a stretch in which the Coyotes had lost five out of seven.
Jiri Tlusty scored for Carolina with 7:45 to go in the middle period, giving the Hurricanes a 3-1 lead.
Korpikoski's goal came with 9:12 remaining and added to the woes suffered this year by Carolina goaltender Cam Ward.
Ward came into the game with a goals-against average of 3.29, which put him 54th among NHL goaltenders in that category.
Jason LaBarbera made 34 saves for Phoenix. Ward allowed the four goals on just 19 shots.