Stoner, who hadn't scored in his first 54 games, put a slap shot from the left point between the legs of Dallas' Jhonas Enroth. The goal was unassisted.
The game was tied at 1 before Stoner's goal at 4:19 of the third. Ryan Getzlaf increased the lead to 3-1 on a breakaway at 14:09.
Corey Perry and Ryan Getzlaf each had a goal and an assist for Anaheim. The Pacific Division leaders are 5-1 in their last six games.
John Gibson made 39 saves for the Ducks, while Enroth finished with 19.
Patrick Eaves scored on the power play for Dallas, which is on a six-game winless streak (0-4-2).