Kiprusoff stopped 11-of-12 shots in the final period, giving Iginla a chance to decide the game on a tie-breaking tally off Alex Tanguay's assist with 7 minutes remaining.
Roman Cervenka scored twice for the Flames, who snapped a three-game losing streak.
Vladimir Sobotka and T.J. Oshie scored for the Blues, who hold the sixth playoff seed in the Western Conference.
Jaroslav Halak yielded three goals on 17 shots.
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