Philipp Grubauer made 15 saves and earned the victory for the Avalanche after replacing Hunter Miska, who allowed four goals on seven shots in the first period.
"Hunter would like to make another save or two in the first period, but I think we hung him out to dry," Colorado coach Jared Bednar said. "It's not something you want to do with a young goaltender who's coming in and trying to build some confidence."
Adam Henrique had a goal and two assists, Troy Terry had a goal and an assist, and Ryan Miller made 28 saves for Anaheim (8-16-6), which has lost four in a row.
"Giving up seven goals is not what you set out to do," Ducks captain Ryan Getzlaf said. "Had a great first period with four goals, which is a big outbreak for our team, but we didn't do a good enough job around our net. They had a lot of chances in the first period. [Miller] made some saves, they hit some posts and we had a chance to win the hockey game. I felt we didn't protect our net."
Burakovsky gave the Avalanche a 1-0 lead at 1:01 of the first period.