Minnesota moved three points ahead of Colorado and the Dallas Stars for first in the division. The Avalanche and Stars each have one game in hand.
"We played like us," Wild coach Dean Evason said. "We didn't play their game. We didn't deviate from the way we play."
Frederick Gaudreau scored two short-handed goals for Minnesota (44-22-9), which is 5-0-1 in its past six games and has earned at least one point in 20 of its past 21 (16-1-4).
"We knew coming in it would be a tough game," Gaudreau said. "The crowd was very loud. It was a fun game to play, and it feels good. I think the thing that feels the best is I think we did it the right way. We were focused for the whole game, and it's fun to get the result from an effort like that."
Bowen Byram and Lars Eller scored, and Alexandar Georgiev made 25 saves for Colorado (44-24-6), which had won three straight.
"I felt like we had some passengers for the first period plus, and when you're playing a game like this, like a playoff-style game, you can't have passengers," Avalanche coach Jared Bednar said. "It's a game of mistakes, and we made some big ones. Didn't make a lot of them, but we made some big ones and they capitalized on them."