Getzlaf stuck a wrist shot inside the right pipe past Marty Turco for the deciding goal. Regulation ended in a 1-1 tie after Anaheim's Corey Perry tied it at 15:01 of the third period with his eighth goal this season.
Jonas Hiller was credited with 31 saves on 32 shots in regulation for the Ducks, who snapped a two-game skid.
Dallas' lone goal was scored by Loui Eriksson at 10:09 of the second. Before Turco gave up the game-winner, he made 23 saves on 24 shots in regulation for the Stars, who have lost four of five.
On the power play, Anaheim went 2-for-4, and Dallas failed to score on eight man-advantage chances.
There were 22 penalties in the game, including 12 by the Ducks.