Jeremy Lauzon scored, and Juuse Saros made 25 saves for Nashville (7-10-0), which has won its past two games after losing four in a row.
The Predators outshot the Avalanche 14-6 in the third.
“We’ve had a few of those go the other way on us,” Nashville coach Andrew Brunette said. “Maybe the hockey gods kind of rewarded us. I think for us, I’m proud of the group. With where we are right now, you’re losing some games and you’re down 3-2 against a really good hockey team.
“What I really liked is we didn’t change the way we played. We had a little bit of belief that we were going to get some looks and we stuck to the game plan.”
Valeri Nichushkin had a goal and an assist, and Cale Makar had three assists for Colorado (11-6-0), which had won three straight. Alexandar Georgiev made 26 saves.
“I thought we made adjustments throughout the course of the game that got us playing better in the second,” Avalanche coach Jared Bednar said. “In the third, I liked a lot of it. Obviously, [an] unfortunate result when you play that hard and you’re in a position to win the hockey game with a few minutes left.”