The Avalanche moved into a tie with the Stars, who have played one more game, for second place in the Central Division. Both teams are one point behind the Minnesota Wild, who lost 4-1 to the Vegas Golden Knights on Saturday, for first place.
Nathan MacKinnon scored two goals, and Alexandar Georgiev made 26 saves for the Avalanche (45-24-6), who have won four of five.
"I thought we had a really good team effort tonight," Colorado coach Jared Bednar said. "And start to finish, too, like full 60, competitive, detailed, very disciplined with the puck. I felt like we managed the puck pretty well. You're not going to win every game, but I do feel like your response after a loss (4-2 to the Wild on Wednesday) is huge."
Tyler Seguin and Joe Pavelski scored, and Jason Robertson had two assists for the Stars (41-21-14), who had won two straight. Jake Oettinger made 27 saves in his second start in as many nights after a 5-2 win at the Arizona Coyotes on Friday.
"Considering the circumstances, we came out ready to play, and we knew what was at stake and played well," Dallas coach Peter DeBoer said. "The errors we made, turning a puck over, taking a too many men on the ice penalty, that's a team that makes you pay for that. I think some of those are fatigue mistakes, but I think there was a lot of good things, too. And I think everyone knows that you're going to have to beat those guys in order to get through the West."
MacKinnon gave the Avalanche a 1-0 lead at 8:54 of the first period. Rantanen stole the puck in the right corner and passed to MacKinnon, who scored with a one-timer after being left all alone on the inside edge of the left circle.
"The pass was elite, and 'Nate' moved right in after he [dumped] it down. He didn't hang around at the blue line and hope for something different to happen," Bednar said. "He drove right into like the best scoring area that there is, right between the hash marks, and capitalized on it. Plus the shot was elite. It was on and off his tape."