The Avalanche have lost eight games when leading after the second period (23-6-2).
"I think when you go into the third period up a goal, it doesn't matter what happened in the second," Avalanche forward Matt Duchene, who had a goal and an assist, said. "You've got to reset and come back out. It has been a problem for our team, closing out games, and [Saturday] was no different."
The Jets (28-35-5) won for the second time in their past 10 home games (2-7-1). Goaltender Ondrej Pavelec made 35 saves.
Erik Johnson also scored for the Avalanche (35-31-4), and Varlamov had 27 saves.
"Give them credit," Duchene said of the Jets. "They played well in the third, but we've got to find a way to calm things down and push back at the right time. We didn't do that."
"[Winnipeg] is going to be a non-playoff team, and not to say that they're not a good team, but we've got to be more desperate than them at this time of year. We have a lot more to play for right now. Giving up that game is not what is going to get us into the playoffs, so it's unfortunate."