Despite earning a standings point, the loss pushed Anaheim's winless streak to 11 games and dropped the club to 27-30-12 (66 points) on the season. The Ducks have 13 games remaining on the regular-season schedule, five at Honda Center.
"I didn't think we were ready to play," head coach Dallas Eakins said. "We didn't come out in that first period with a lot of anger, but we did get that. I thought we played better after the first."
John Gibson stopped 31-of-34 shots in his 49th start. Kevin Shattenkirk and Jamie Drysdale scored for Anaheim.
"I think right now it's a little bit of a tough stretch," Drysdale said. "We just gotta stay positive, take away what we can, learn from the things we can work on and move forward from there."
The win moved Dallas back into the second Wild Card position, one point ahead of Vegas. The Stars are also just four points out the Central Division's third automatic playoff spot.
Jake Oettinger made 21 saves to earn his fourth win in his last five games. Oettinger stopped 47-for-51 in the two-game set against Anaheim, his first two career appearances against the Ducks.
Benn, Ryan Suter and Andrej Sekera scored for the Stars, who have now won five of their last six games.
Dallas went ahead first midway through the opening period when Suter got to a rebound in the slot and deposited it past a sprawling Gibson for a power-play goal.
The Ducks pulled back even in the final minute of the middle frame on one of the strangest goals of the entire season. Following an icing call against Dallas, Anaheim corralled a faceoff to Oettinger's left, working the puck back to Drysdale at the right point, who quickly directed a shot towards the goal. Drysdale's bid missed the net but kicked off the end board back to the crease, where it bounced off Oettinger's skate along the goal post and just over the line.