Ray Whitney of the Coyotes grabbed control of the puck from a pair of defenders behind the Dallas net shortly after a face-off in the Stars' zone.
The Phoenix forward then found Vrbata alone at the top of the crease, and the Coyotes' leading goal-scorer netted his 28th of the year after skating in on goalie Kari Lehtonen, faking him to the ice and shooting it into an empty net.
Mikkel Boedker got the Coyotes' only regulation goal and Mike Smith turned aside 30 shots as Phoenix extended its point streak to eight games (7-0-1).
The hot streak has lifted the Coyotes to within two points (67) of idle San Jose in the Pacific Division.
Lehtonen finished with 31 saves and Michael Ryder scored for Dallas.