Kyle Brodziak scored 6 minutes into the contest and Cullen doubled the advantage 10 minutes later, getting behind the Anaheim defense on an odd-man rush and converting a Cal Clutterbuck pass into a goal.
Jared Spurgeon closed out the Wild's scoring with 29 seconds remaining on a slap shot from the left point as Minnesota moved past Edmonton into first place in the Northwest Division with the win.
Niklas Backstrom turned aside 32-of-34 shots to earn the victory.
Cam Fowler scored twice for Anaheim, including with 49 seconds left to cut the deficit to one goal, but the Ducks could get no closer.
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