The Ducks overcame a three-goal deficit in the third period to force overtime and win for the eighth time in their last 10 games.
Bobby Ryan scored a pair of goals for Anaheim, including the tying score with 30 seconds to play in regulation. Ryan knocked in a rebound off a shot by Ryan Getzlaf.
St. Louis took a 3-0 lead at 3:35 of the third period on a goal by T.J. Oshie. Andy McDonald and B.J. Crombeen scored in the second period.
Scott Niedermayer began the comeback with a goal less than two minutes after Oshie scored. Ryan then scored his first goal at 12:00 of the third and tied at 19:30.
Hiller finished the game with 18 saves. Mason stopped 34 shots.