Reinprecht's goal came with 13:10 to play, but Niklas Backstrom shut the door on the Coyotes and Clutterbuck restored a two-goal lead with 6:36 to play. James Sheppard added a score on a tip-in with 4:44 to go.
Backstrom finished with 21 saves.
Marc-Andre Bergeron, who had been out of action since Dec. 19 with a lower body injury, scored Minnesota's first goal in his return.
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