Trailing 2-0 in the middle frame, Minnesota began its comeback when Dany Heatley tallied on a slap shot 9:35 into the period.
Zucker tied the score less than 4 minutes later with his first career goal -- an unassisted tally -- and Mitchell quickly followed with a backhander after a face-off for the decisive score.
Darcy Kuemper earned his first NHL victory, turning aside 29-of-31 shots for the Wild, who snapped a two-game skid.
Damien Brunner and Pavel Datsyuk scored and Petr Mrazek -- playing in his second career game -- made 21 stops for the Red Wings.
2014: The Year in Music [PHOTOS]