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.
Exploding whale video goes viral on Internet
Texas principal bans speaking Spanish, stirs controversy