The Stars had the first good scoring chance of the game at the 4:12 of the first period but Mike Smith snatched the shot away with a quick glove.
Phoenix would get three chances on the power play in the first period but would not convert on any of the man-advantage opportunities.
The lone goal of the period would come off the stick of of Mikkel Boedker at 13:31. The assists came from Lauri Korpikoski and Keith Yandle and it was Boedker's eight of the year.
The Coyotes have been bit by the injury bug lately. With veteran defenseman like Derek Morris and Rostislav Klesla out of the lineup, Chris Summers and recently recalled Michael Stone have been forced to assume a more prominent role defending the Coyotes blue line.
At 10:41 of the first period Summers took a interference penalty which led to a Dallas goal. Michael Ryder put the power play goal in towards the end of the power play for his 22nd of the year.
After a combined 62 shots through regulation, the teams would need overtime to decide a winner.
The combination of Ray Whitney and Vrbata has become something Coyote fans have got use to hearing, and Saturday night the duo would be at it again; but for the overtime game winner. Whitney found Vrbata with an amazing pass in the slot and Vrbata dangled the goalie far to the right, easily putting away the goal.
The goal was Vrbata's 28th and Whitney's team-leading 52nd point.
Mike Smith shined again in net for the Coyotes. The streaking Smith did have a goal scored on him, breaking his consecutive shutout streak, but Smith managed to stop 30 shots in the win.
The Coyotes are now riding a eight game streak of earning at least a point and gained a valuable point on their Pacific Division foe. The 'Yotes are now only two points out of sixth place.
Next Tuesday the Coyotes take on the Los Angeles Kings at home. The game comes less than a week after the two teams had a heated exchange in Los Angeles, so tensions are expected to be high.
The puck drops at 7 p.m at Jobing.com Arena and can be seen on Fox Sports Arizona.