Datsyuk put a rebound past goalie Antti Niemi at 2:33 of overtime while Mattias Janmark was off for hooking. Detroit moved into third place in the Atlantic Division, one point ahead of Boston.
Dallas’ Vernon Fiddler put in his own rebound to tie the score with 1:31 to play in the third period. The Stars had an extra skater on after pulling Niemi. Fiddler also assisted on Colton Sceviour‘s second-period goal.
By earning one point for the overtime loss, the Stars tied Chicago atop the Central Division.
Howard made 39 saves, and Niemi had 30.
Datsyuk has 49 points (19 goals, 30 assists) in 41 career games against the Stars. Detroit had failed to score in its last 20 power plays over seven games.
The Red Wings have won their last seven games in Dallas dating to Oct. 14, 2010.
Athanasiou gave the Red Wings one-goal leads in both the second and third. He had only two goals in his 17 previous NHL games.
Dallas outshot the Red Wings 15-7 in a scoreless first period. Detroit didn't have a shot on goal for the first 6 1/2 minutes.
The Stars' best chance came 17 1/2 minutes into the game when a deflected shot by Jason Demers bounced off the left post.
Each team had one power play in the first.
Both teams scored in the second period. Detroit's Gustav Nyquist took a shot from the slot and the puck was deflected. It rebounded into the right faceoff circle, where, Athanasiou sent a wrist shot past Niemi.
Sceviour tied it 1-all at 17:32. Fiddler passed across the goal mouth, and the puck bounced off Sceviour's right shin into the net. A video replay confirmed that he did not kick the puck.
The Stars again outshot the Red Wings, 14-10.
Athanasiou scored again at 6:38 of the third period. He skated past Dallas defenceman Johnny Oduya, moved the puck to his backhand and skated in front to shoot over Niemi.
NOTES: Red Wings G Petr Mrazek was scratched because of a groin injury. General manager Ken Holland said the goalie is day to day. . Howard had been 0-5-4 since his last win. . The Red Wings brought up Jared Coreau from Grand Rapids of the AHL to back up Howard. . Sceviour has scored three of his eight goals in the last three games. . Fiddler played in his 800th game.