With the Flames trailing 1-0 in a tight-checking affair, Olli Jokinen fed Iginla in the slot, where Iginla used his skate to position the puck for a backhander past Steve Mason 3 minutes into the final frame.
In the first round of the shootout, Iginla skated in on Mason, made a series of fakes and pulled the puck to his forehand for a quick shot and a goal.
Kiprusoff finished with 27 saves for the Flames, who won their fourth straight.
Derick Brassard scored and Mason made 25 saves for Columbus.
Megyn Kelly: Santa Claus and Jesus are both white men
Costly malfunction causes beer flood at Boston-area brewery