Vrbata put a high backhander past Chicago goalie Corey Crawford in the second round of the tiebreaker, and Ilya Bryzgalov made the advantage hold up for a win when he stopped Patrick Kane and Marian Hossa missed on the Blackhawks' final try.
Vrbata also scored a regulation goal for Phoenix, as did Taylor Pyatt. Bryzgalov turned away 31-of-33 shots as the Coyotes won their fourth straight and stayed in the thick of the Western Conference playoff scramble.
The defending Stanley Cup champion Blackhawks, meanwhile, sank further out of playoff contention with their sixth loss in eight contests and second straight shootout setback.
Duncan Keith and Troy Brouwer scored and Crawford made 23 saves for Chicago.