Hampus Lindholm's power-play goal broke a 1-1 tie with 5:56 left in regulation to lift Anaheim past Colorado at Pepsi Center in Patrick Roy's debut as an NHL coach.
Devante Smith-Pelly also scored for the Ducks. John Gibson earned the victory by stopping all 18 shots he faced in relief of Frederik Andersen, who made nine saves.
Paul Stastny gave the Avalanche a 1-0 lead 13:15 into the game by tipping Alex Tanguay's shot past Andersen.
"We worked hard and I thought we competed well," Roy said. "Defensively we were good."
Semyon Varlamov stopped 22 of 24 shots for Colorado.