The goal, Lehtinen's second of the game, stood up after a dispute and video review.
During a goal-mouth scramble with time expiring, Lehtinen appeared to knock the puck in the net with his stick above his right shoulder Referee Tom Kowat, after consulting with replay officials, declared the goal good and Dallas skated off with its fifth straight victory over Phoenix, spanning two seasons.
Phoenix came from two goals behind in early in the second period to eventually tie the game.
With Dallas leading 3-2, Mike Zigomanis got the Coyotes even when he knocked in Ladislav Nagy's shot from the right circle at 7:46 of the third period.
Though the Coyotes had the early territorial edge, Dallas scored two power-play goals in the first period.
Lehtinen converted a centring pass from Jussi Jokinen to beat Phoenix goalie Milkael Tellqvist at 8:48. Dallas struck again with the man advantage when Jokinen took Lehtinen's pass and redirected the puck in at 12:11.
The Coyotes, shut out in their first three games against the Stars this season, finally scored when defenceman Ed Jovanovski's shot from the left point found its way through traffic and past Marty Turco at 13:37.
The team traded second-period goals.
The Stars made it 3-1 when Niklas Hagman drove Jovanovski off the puck behind the Phoenix net, circled in front, and beat Tellqvist with a backhand shot just 42 seconds into the period.
The Coyotes cut the margin to 3-2 as Owen Nolan, off a pass from Jeremy Roenick, beat Turco with a wrist shot at 6:37.
Notes: Stars forwards Mike Modano, Brenden Morrow and Eric Lindros sat out with injuries. ... Phoenix allowed 31 shots in the first two periods. The crowd of 15,320 was only the fifth for Phoenix this season above 15,000. The Coyotes have not sold out a home game this season.