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.
Notable deaths of 2014 [PHOTOS]