Poehling scored on a rebound in the crease to tie it 1-1 at 3:32.
Hintz found an opening in the high slot and scored with a wrist shot to give Dallas a 2-1 lead at 4:42.
Steel extended the lead to 3-1 at 12:41. He drove to the Anaheim net and collided with the right post just as the puck went off the stick blade of Trouba and fluttered across the goal line.
The posts came off their pegs just before the puck crossed the goal line, but the goal was upheld after a video review.
"I just saw the post coming at me," Steel said. "Ran out of options."
Harley ended Dostal's night when he scored with a wrist shot from the right circle to extend the lead to 4-1 at 14:19.
“That's one of the best teams in the league and we let them just play their game," Ducks captain Radko Gudas said. "We weren't making it hard for them to get pucks through and we screened our own goalie, so it was very hard today for the tendies.”