Dallas has won all seven meetings with Atlanta since the Thrashers joined the NHL for the 1999-00 season. The Stars have outscored the Thrashers 23-12 in those meetings, including three home wins.
Dallas has gone 0-1-4 since winning a season-high four straight from Dec. 20-27. On Monday, the Stars blew a 2-1 lead in the third period for the third time in four games, settling for a 2-2 tie at Anaheim.
The Stars took the lead with 14:53 left in the third on Scott Young's third goal of the season, but the Ducks tied it midway through the period.
Dallas, which hasn't scored more than two goals in 16 of its last 20 games, came up empty on all five power plays, making it 0-for-13 with the man advantage in its last three games.
"With all the power-play opportunities, we should have put them away, but we didn't," Young said. "We tried to keep their shots down to about 20 -- and that's good, as long as they're not quality shots."
Atlanta's losing streak reached a season-high four games Saturday, falling 5-1 to the Montreal Canadiens in the second game of its five-game road trip.
The Thrashers, who have allowed five or more goals in three of the four losses, have been very streaky offensively, and are in the midst of another scoring funk.
Atlanta had scored 14 goals during a three-game winning streak from Dec. 20-26, but has scored just nine times during its four-game skid.
The Thrashers, who lead the Tampa Bay Lightning by four points for first place in the Southeast Division, conclude their trip with matchups against the San Jose Sharks and Phoenix Coyotes this weekend.