A 19-year-old defenseman, Schultz opened the scoring 5:38 into the contest, chipping a puck past goaltender Roberto Luongo to start Minnesota's barrage. Schultz had just two assists in his previous 14 games this season.
Andrew Brunette collected three assists for normally defensive-minded Wild, who scored six goals for the second time this season and fourth time in their two-year history.
Pascual Dupuis added a goal and an assist for Minnesota, which has won four of its last five games.
Dwayne Roloson stopped 29 shots for his second shutout of the season and fourth of his career.
Luongo surrendered five goals on 14 shots before being pulled with 7:46 left in the second period. Florida has lost three straight and five of its last six games (1-4