The contest was deadlocked 3-3 after Vrbata's seventh goal of the season (power play) with just over one minute left in the third period. Phoenix also got a goal from Peter Mueller in the first.
Vrbata added an assist, and recently-signed goaltender Ilya Bryzgalov stopped 23-of-26 shots in regulation, and two in the shootout, as the Coyotes bagged their first three-game winning streak this season.
Anaheim's Chris Pronger scored twice, with his second of the contest -- and third of the season -- giving his team a 3-2 lead at 2:53 of the third.
Ryan Getzlaf scored unassisted at 12:52 of the first, while goalie Jonas Hiller -- making his third NHL start -- stopped 35-of-38 shots in regulation, but could not stop Vrbata's wrist shot shortly after Pronger's slashing penalty.
Phoenix rose to 3-1 in the season series.
Celebrity Families of 2014 [PHOTOS]