"Somebody had to come in here and break the streak," Stars coach Rick Bowness said. "We're the team to do it."
Nathan MacKinnon scored, and Pavel Francouz made 16 saves for the Avalanche (34-9-4), who had their home point streak end at 22 (20-0-2). Colorado's last loss at home was Oct. 26, 3-1 to the Vegas Golden Knights.
"I thought we created plenty [of] scoring chances to win the hockey game," Colorado captain Gabriel Landeskog said. "First period, we gave up odd-man rushes, which we don't like to do and shouldn't do. I thought after that we limited their scoring chances for the most part."
Jake Oettinger made an NHL career-high 46 saves, and Joe Pavelski scored twice for the Stars (26-19-2), who have won their past five road games.
"[Colorado is] the best team in hockey, and you're playing with, like, half your lungs out there pretty much (due to the altitude), so I knew I was going to have to weather the storm a little bit," Oettinger said. "The guys just did so many good things in front of me.
"If they let me see [the puck] and tie up guys around the net, then I think we'll have success. Ton of blocks, and a couple of saved goals, and all around it was just huge for our team."