Sergei Kostitsyn's goal near the end of the winner as the Nashville Predators skated 2, on Thursday at Bridgestone Arena.
The Predators remain entrenched in the fifth spot in the Western Conference with 85 points, four behind Detroit for fourth place.
"I think we had a much better effort," Predators head coach Barry Trotz said. "We wanted to get off to a good start. They scored right away, but I thought we responded really well, and the rest of the period we were really good."
Paul Stastny had a goal and an assist, while Jamie McGinn also lit the lamp for the Avalanche, who had their brief two game winning streak snapped. The Avs are a point out of the last playoff spot.
Kostitsyn's game-winner came with just 32 seconds left in the second period as a result of a poor pass in the Colorado zone. Gabriel Landeskog took the disc around behind his net and looked for the breakout pass, but sent it straight up the middle of the ice and it was picked off by Kostitsyn.
Kostitsyn then glided to the slot and ripped a wrister past Varlamov to give Nashville a 3-1 advantage.
The Avs made it a one-goal game again just 4:58 into the third period after Stastny got a perfect feed in the slot from Peter Mueller and beat Rinne with a quick wrist shot, but Martin Erat put the game away with an empty-netter with 44 seconds to play.
Colorado opened the scoring just 1:14 into the contest after David Jones chased down a loose puck in the right corner and quickly sent it in front for McGinn to tap home.
The Preds tied it less than two minutes later when Shea Weber brought the puck into the offensive zone on the right wing and dropped it for Fisher, who threw a shot on net that got past a screened Varlamov.
Nashville took a 2-1 lead at 6:58 of the second period after Roman Josi fired a slap shot from the point that was tipped past Varlamov by Yip, who provided a perfect screen in front.
Nashville improved to 13-2 this season in games decided by two goals...The Preds have posted a 25-20-6 record in 51 games all-time against the Avs. They are 14-9-3 all-time on home ice against Colorado...Prior to Thursday's game, the Avs announced that forward Matt Duchene will miss 3-4 weeks with an ankle injury...The win was Rinne's 37th this season, which is a new franchise record for most wins by a goalie in a single season...The Preds failed to score on two power-play chances, while the Avs did not have any man advantage opportunities.