Alex Tuch scored two goals, and William Karlsson had two assists for Vegas (11-4-1), which earned a split of the four-game set after losing the previous two games.
Philipp Grubauer made 25 saves for Colorado (9-5-1), which won its previous four games at Ball Arena and was coming off a 3-2 victory against Vegas in the Bridgestone NHL Outdoors Saturday at Edgewood Tahoe Resort in Stateline, Nevada.
"We had some chances, we just didn't capitalize on them," Avalanche defenseman Cale Makar said. "Obviously, Fleury's always going to have a good night, and you have to be prepared for that, but I think this one lies on us more than anything. We made some mistakes, especially me personally, and we definitely have to tighten up in the [defensive] zone a little bit."
Tuch moved up to the No. 1 line, taking Max Pacioretty's regular spot with Chandler Stephenson and Mark Stone, and helped shut down the Avalanche's top line of Andre Burakovsky, Nathan MacKinnon and Mikko Rantanen.
"You have an elite skater like that, stick-handler, shooter," Tuch said of MacKinnon. "The guy's world class. A lot of plays are going to go through him, and we know that because of how good he is. We didn't want to give him any time and space. We wanted to frustrate him as much as possible. I guess we were out there a lot against him. It was great."
DeBoer said, "Tuch's had a great year. He's earned everything he's got with hard work and coming prepared to have a good start to the season. He's a really effective guy. I liked him as much defensively tonight as I did offensively. With his speed defensively, he's one guy that can really hunt down guys like MacKinnon from behind because he has that speed. I thought he was very effective defensively, as well as the two goals he kicked in for us."