The Coyotes got a 30-save effort from Sean Burke, who went in leading the NHL in most goaltending categories. Phoenix was unable to score with a man advantage for the fourth straight game since special-teams quarterback Joe Juneau injured his shoulder.
Trevor Letowski had a short-handed goal for the Coyotes, and Shaun Van Allen and Joe Nieuwendyk scored for the Stars.
Phoenix is 7-0-4 since its only loss of the season. During the streak, the Coyotes have been outshot 10 times, including 32-17 by the Stars.
But it took just 12 shots for the Coyotes to get their second goal against Dallas goalie Ed Belfour, who shut out Columbus on Wednesday.
Dallas outshot the Coyotes 14-4 in the first period, and this time it was too much for Burke, the NHL's player of the month in October.
He stopped the first 11 shots, but was falling to the ice when Van Allen lifted his own rebound into the top of the net as Burke sprawled across the goal mouth with 3:1left in the first period.
The Coyotes lost Juneau with a shoulder strain and played this game without Tkachuk, who experienced back spasms during warmups.
As a result, they were scoreless in three power plays and are 0-for-14 without Juneau.
It didn't hurt their penalty killers, though. Letowski, who set a franchise record for short-handed goals by a rookie (four) last season, got his first goal while the Stars had a 5-on-3 advantage.
He got the puck in the neutral zone when a pass by Dallas hit the skate of Juha Ylonen and deflected to him. Letowski sped to the circle and fired a wrist shot that drifted in between Belfour's legs with 7:14 left in the second period.
But Dallas still had 1:22 left in its fourth power play, and the Stars capitalized with five seconds left.
Brenden Morrow sent a pass from high in the circle to Nieuwendyk, who redirected it past Burke on the near side with 5:57 remaining in the period.
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