Fontaine scored late in the first period, gave the Wild a two-goal lead on a power play in the third and closed out his first career hat trick with an empty-net goal.
Kyle Brodziak had a goal and an assist, Matt Cook had two assists and Backstrom won his third straight start after allowing 17 goals the previous four.
Mikkel Boedker scored for the Coyotes, who have lost three of four.
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