Jonas Hiller stopped 25 shots for the NHL-leading Ducks, who were shut out for the first time all season. Anaheim has lost three of five at Honda Center after opening the season 20-0-2 at home.
Ellis had sat out the Stars' previous nine games since Jan. 12, but Kari Lehtonen's veteran backup posted Dallas' third shutout victory in its last six games. Ellis played 23 games with Anaheim from February 2011 to 2012.
Captain Jamie Benn added an empty-net goal with 28 seconds left for the Stars, who snapped a five-game road skid.
The Ducks played without third-leading scorer Nick Bonino after the versatile centre injured his wrist during Thursday's victory over Philadelphia. Anaheim recalled veteran David Steckel to fill in, but coach Bruce Boudreau also scratched healthy offence-minded forwards Dustin Penner and Kyle Palmieri.
Anaheim began a stretch of four games in eight days before the Olympic break looking to maintain its position atop the league, but the grind of the regular season is finally hitting the Ducks after two spectacular months. Anaheim is 4-4 since Jan. 15, but still leading defending champion Chicago in the overall standings.
Dallas also is looking to build momentum into the break during a three-game West Coast trip over the next five days. The Stars began the day in an 11th-place tie in the Western Conference.
Only Hiller kept the score close with a handful of stellar plays in the final two periods, including a post-to-post toe save on Rich Peverley late in the second. Hiller has lost his last three home starts after his franchise-record 14-game winning streak ended last month.
Anaheim had several decent chances in the final minutes, but was shut out for the first time since last March 27. Corey Perry had the puck with a look at an open net after the Ducks pulled Hiller, but the Canadian Olympian couldn't score.
The Ducks also lost defenceman Mark Fistric to a lower-body injury early in the game.
NOTES: Along with Bonino, the Ducks had three prominent healthy scratches who have combined for 90 points this season: Penner, Palmieri and D Bryan Allen. ... Just 41 seconds in, Eakin skated to the Stars dressing room with a bloody cut on his face after he got hit by the puck. He returned for the second period. ... Daley has three goals in his last 10 games after scoring just once in his first 31 this season.