Vrbata twice gave the Coyotes a two-goal lead, his second goal coming on the power play with just 23 seconds left in regulation to seal the victory.
Mikkel Boedker produced the other Phoenix goal and Thomas Greiss saved 28 shots.
The only Minnesota goal came from Dany Heatley in the second period that brought the Wild within 2-1.
Minnesota had won its previous six games at home. The loss was suffered by Niklas Backstrom, who stopped 23 shots.