Nathan MacKinnon scored the go-ahead goal in the third period, and Blake Comeau and Mark Barberio scored for Colorado (23-16-3, 49 points), which surpassed its win and point totals from last season (22-56-4, 48 points).
Nikita Zadorov had two assists, and Jonathan Bernier made 27 saves for the Avalanche, who have their longest winning streak since they won six in a row March 25-April 5, 2014.
WATCH: [All Avalanche vs. Stars highlights]
"I think our guys are hungry to try and keep this thing going, so that's a big factor, and it showed tonight," Avalanche coach Jared Bednar said. "We were disciplined, we were determined. I liked the compete level right off the bat. We had a good start and it carried for the rest of the game. Our guys were talkative on the bench. They played the game with emotion tonight. They're starting to come together as a team."
Jamie Benn scored, and Ben Bishop made 19 saves for Dallas (24-17-3), which like Colorado was playing its first game after a six-day break.
"We just didn't have that extra push that we've been having lately," Stars forward Tyler Pitlick said. "When you're not feeling great, we've got to find a way to make it happen anyways and find plays and play hard. So that's something we've got to figure out."