The Avalanche scored four times in the second period to take a 5-0 lead while handing the Wild their fifth straight loss.
Devin Steoguchi's penalty shot ended the shutout bid of Varlamov, who made 21 saves.
Josh Harding got the start in goal for Minnesota, but he was removed after giving up three scores on 18 shots. Matt Hackett fared no better in relief, allowing four goals on 21 shots.
Lytro unveils camera that can focus a photo after shooting it
Moore to attend retreat in to avoid Kutcher's wedding