Rick Nash and Kyle Wilson both beat Jose Theodore in the first two rounds of the shootout but Pierre-Marc Bouchard extended the affair with a dipsy-doodle backhander past Blue Jackets netminder Steve Mason.
Huselius ended the game with a shot past Theodore and the Blue Jackets won for just the second time in eight games.
Derick Brassard, Fedor Tyutin and Andrew Murray got regulation-time goals and Mason finished with 36 saves in the win.
Minnesota's Cal Clutterbuck forced overtime when he scored to make it 3-3 with 8:22 left in the third period.
Chuck Kobasew and Mikko Koivu also found the net and Theodore turned aside 19-of-22 shots for the Wild.