Heatley raced in on Coyote goaltender Jason LaBarbera, shifted to his backhand and slipped the puck into the net to put an end to Minnesota's five-game losing skid.
Kyle Brodziak and Steven Kampfer accounted for Minnesota's two goals in regulation and Matt Hackett allowed two goals on a 17 shots.
LaBarbera allowed two goals on 24 shots. Raffi Torres and Lauri Korpikoski scored for the Coyotes, who lost their fifth in a row.
Both Phoenix goals came in the third period and tied the score 2-2, after Minnesota had taken a 2-0 lead with a pair of goals a minute apart in the first period.