Jason Robertson tied it 2-2 for Dallas with 26 seconds remaining in the third period on a shot from the bottom of the right face-off circle.
"We shouldn't have given up that extra point, that's my fault on that one," Colorado defenseman Cale Makar said. "Just bad coverage read, and then right off my stick far-side. That game should have been ended in regulation. I feel like we outplayed them for most of the night, gave them a couple of chances, but overall, I feel like we minimized it as a group."
Makar and Alex Newhook scored, and Alexandar Georgiev made 22 saves for the Avalanche (11-5-1), who swept a three-game road trip and have won seven of their past eight games. Mikko Rantanen had the only goal in the shootout.
"It's huge for us, huge," Newhook said. "Obviously a time where we're trying to build and missing a lot of guys in our lineup. But guys are stepping up, and to get six points on a trip where we're playing three pretty good teams, that's huge for us."