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.
Swim Week Miami Beach 2014 [PHOTOS]