It was the first tilt of a four-game homestand after returning from a five-game Stateside road swing.
Tyler Toffoli picked up his 16th goal of the season in the contest, while Jacob Markstrom made 26 saves.
Alexander Georgiev turned aside 34 pucks at the other end of the ice, coming up massive in the final frame to hold back the Flames onslaught.
Calgary product Cale Makar missed the game for the Avs, out with an injury and listed as day-to-day.
Walker Duehr had a good look with a backhand on the doorstep early in the first period that Georgiev gobbled up, then later Elias Lindholm came flying in from the blueline and stepped into a one-timer that was turned aside.
Mikko Rantanen opened the scoring at 6:17, wiring a shot from the left faceoff circle that beat Markstrom for his 30th goal of the season.
The visitors doubled their lead off a 2-on-1 at 11:02, Nathan MacKinnon feeding the puck across to Arturri Lehkonen who tallied, although the officials originally didn't signal a goal but after review sent the players to centre ice for the faceoff.
Lehkonen gathered a rebound off the end boards and put it shortside on the powerplay at 12:58 to increase the Colorado lead.
Rasmus Andersson came close to getting Calgary on the board when he wired one of the crossbar near the midway point of the second period.
Toffoli fired a perfect wrister high gloveside past a screened Georgiev on the powerplay at 2:27 of the third period, with Andersson and Lindholm picking up the helpers.
