Valeri Nichushkin tied it 3-3 at 4:19 in the third period on a tap-in from the slot.
Mikko Rantanen gave Colorado a 4-3 lead at 14:32 when his shot deflected off of Stars forward Evgenii Dadonov, and 11 seconds later, Andrew Cogliano made it 5-3, sweeping the puck into the net as it sat on the goal line.
Cale Makar had three assists, and Alexander Georgiev made 24 saves for the Avalanche (11-5-0).
Tyler Seguin had two goals, and Mason Marchment had two assists for the Stars (11-4-1). Jake Oettinger made 32 saves and allowed more than three goals for the first time this season.
Seguin gave Dallas a 1-0 lead at 10:33 in the first period when Marchment found him on the back door from below the goal line.
Joe Pavelski made it 2-0 on the power play at 14:21 on a one-timer from the slot off a pass by Jason Robertson.
Seguin extended the lead to 3-0 at 2:12 in the second period on a rebound from the bottom of the right face-off circle.
Miles Wood cut the lead to 3-1 at 13:27 on a breakaway, and Ryan Johansen cut it to 3-2 at 17:09 on a tipped shot from the slot on the power play.
Ross Colton scored into an empty net at 19:30 for the 6-3 final.
