Vrbata's goal at 3:35 in the third period gave Phoenix a 3-1 lead that held up after Matt Niskanen scored the Stars' second and final goal of the game on a power play at 7:02.
Robert Lang and Davis Schlemko also scored for the Coyotes, who snapped a two-game losing streak.
Mike Modano scored a goal and added an assist for Dallas. Marty Turco had 28 saves in goal.
Modano's goal came six minutes after Lang had opened the scoring a mere 12 seconds into the second period.
Schlemko scored with 25 seconds left in the second period to give the Coyotes a 2-1 lead.
Ilya Bryzgalov finished with 26 saves for Phoenix.
2014: The Year in Music [PHOTOS]