The Blackhawks let a two-goal lead get away in the third period but still ended a two-game skid, won for the sixth time in eight games and inched closer to a playoff spot.
Chicago appeared headed for a regulation victory when Patrick Sharp gave the Blackhawks a 3-1 lead with 11:20 to play. Jason Arnott brought St. Louis within one less than a minute later and David Perron forced overtime by tipping in a shot with 1:32 to go.
The one point the Blues picked up boosted them one in front of the New York Rangers for the best record in the NHL.
Corey Crawford had to make only 17 saves in regulation and was perfect in the shootout to pick up the win. Jaroslav Halak stopped 37 shots.