Vrbata's tally 4:15 into the final period came from a sharp angle to the left of Minnesota goalie Niklas Backstrom, breaking a 1-1 tie.
He found the net again 2 minutes later when his wraparound shot beat a diving Backstrom, and the Coyotes held on to snap a season-worst four-game losing streak.
Curtis McElhinney made 28 saves, including several point-blank shots in the final period, to pull out the victory.
Backstrom ended with 26 stops for the Wild.
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