Trailing 1-0 for much of the game, Anaheim got the equalizer from Pat Maroon 3 minutes into the final frame and Sbisa notched the game-winner with 3:04 left to play.
Jonas Hiller earned the victory with 31 saves as the Ducks improved to 3-0 against Minnesota this season and locked up their fourth straight victory overall.
Devin Setoguchi scored for the Wild, whose four-game home winning streak was halted.
Niklas Backstrom made 19 saves for the Wild.
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