The Avalanche improved to 13-2 for the season and took the lead for good when Ryan O'Reilly opened the scoring 5:31 into the contest.
Giguere has made five starts this year and has won them all. Both of the goals he allowed came in the second period from Mike Cammalleri.
Colorado took a 3-2 lead into the final period and protected it until Matt Duchene scored into an empty net with two seconds remaining.
Karri Ramo gave up three goals on 26 shots to take the loss. The Flames have lost three in a row.