Just by getting into overtime, the Ducks clinched a post-season spot. They then went on to capture the game when Jonas Hiller was able to stop two of Dallas' shootout attempts.
Dallas forced overtime when Steve Ott scored with 14 seconds remaining in the third period.
Anaheim took a one-goal lead on three occasions, getting scores from Todd Marchant, Scott Niedermayer and Andrew Ebbett. Ebbett gave Anaheim a 3-2 lead with 6:04 to play in the third.
Hiller made 42 saves in regulation and overtime.
St. Louis and Anaheim are tied for the seventh spot in the playoff standings with 90 points each. They both have a game left to play.
The team that finishes eighth will meet San Jose in the first round of the playoffs. The seventh-place team will face Detroit.