The Ducks trailed 3-1 after the first period but then scored four of the next five goals to forge a 5-4 lead with less than 7 minutes left in the regulation.
The Blues, however, forced overtime with Chris Stewart scoring on a power-play with 4 1/2 minutes remaining in the final frame.
St. Louis seemed to have won it with 22.2 seconds left in overtime but the goal was disallowed when the referees ruled Ducks goalie Viktor Fasth was prevented from making the save by a player in the crease.
Alex Steen and Stewart each registered a goal and two assists for the Blues. Elliott turned aside 18 shots.
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