Jaroslav Halak, meanwhile, stopped Rich Peverley and Alex Burmistrov in the shootout to hand St. Louis its first four-game winning streak since posting five straight in February and March of last season.
Jay McClement scored three goals for St. Louis and Halak stopped 25-of 28 shots through regulation and overtime time to pick up the victory.
The Flames got a goal and an assist each from Peverley and Nik Antropov, and Niclas Bergfors also scored.
The game marked the return of Flames goalie Ondrej Pavelec, who made his first appearance since suffering a fainting spell Oct. 8 against Washington.
Pavelec made 32 saves Saturday night but yielded a pair of third-period goals to allow the Blues back into the game.