Conor Sheary scored for Washington (15-13-4). Charlie Lindgren, who started each of its five straight victories, made 24 saves.
The Capitals outshot the Stars 30-12 over the final two periods.
"We're going to go back and look at the scoring chances and they're going to be ridiculous, so it's tough," Washington coach Peter Laviolette said. "Our guys are down the road of doing everything they can to win hockey games, and tonight it didn't want to drop for us."
Sheary gave the Capitals a 1-0 lead at 9:23 of the second period. Ovechkin received a pass in the left face-off circle from Dylan Strome and passed across to Sheary, who was cutting to the net. Sheary kicked the puck to his stick and tucked it past Oettinger.
Ovechkin has 10 points (seven goals, three assists) in a five-game point streak.
"Yeah, that's kind of the benefit of playing with [Ovechkin]," Sheary said. "The goalie plays the shot, and I snuck backdoor and was able to tap one in."
Benn tied it 1-1 just 48 seconds into the third when he knocked in a rebound during a power play, and Miller gave Dallas a 2-1 lead at 2:07 with a wrist shot from the right point that deflected off the back of Washington forward Lars Eller and past Lindgren.
"We wanted to regroup," DeBoer said of the difference between the second and third. "We've got an honest group. They know when we're playing well and when we're not. They know how to fix it."