Setoguchi beat Corey Crawford to the glove side for the only shootout score, clinching Minnesota's fourth win in five games.
Chicago, which has lost two straight, will enter the Western Conference playoffs as the No. 6 seed.
With time running down, Cal Clutterbuck scored on the power play for the Wild.
Harding made 22 saves before turning in a perfect shootout performance. Crawford stopped 22-of-23 shots.