Sean Monahan also scored and Karri Ramo stopped 22 shots for the Flames, who broke out of an offensive slump to end a four-game skid.
Calgary came into the game having been shutout in three of its last four games. The Flames' only goal since Dec. 23 came in a 4-1 loss to Philadelphia.
Nathan MacKinnon had two goals and Paul Stastny had a goal and two assists for the Avalanche, who had won three straight coming into the game.
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