Sean O'Donnell scored the overtime goal just 1:36 into the overtime period as a power play was ending.
Jean-Sebastien Giguere blocked 25 shots, giving him an 8-0 career playoff overtime record.
Jarome Iginla tied the game up for the Flames, scoring both their goals in the third period.
Miikka Kiprusoff saved 27 shots in the loss.
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