Kiprusoff allowed a goal by Paul Stastny just 34 seconds into the game, but shut the door after that.
The Calgary goalkeeper was especially busy in the third period as the Avalanche launched 15 shots, weathering a 6-on-4 situation over the final 16 seconds.
Mark Giordano and Curtis Glencross scored for the Flames, who have outscored Colorado 29-11 during their seven-game streak against the Avalanche.
Semyon Varlamov stopped 21 shots for Colorado, which fell to 1-5-0 at home this season.
Celebrity Families of 2014 [PHOTOS]