The Avalanche ended a four-game losing streak. They began the night just two points out of a tie for eighth place in the Western Conference, but they now have only two games left in which to compile enough points to reach the playoffs.
All of teams they are fighting for the post-season berth have four games remaining.
Mark Olver and David Jones both scored in the opening period for Colorado and Milan Hejduk provided a second-period goal.
Jarome Iginla ended Varlamov's shutout bid by scoring on the power play with 38 seconds to play. Peter Mueller then tallied into an empty net for the Avalanche.
Calgary's playoff hopes have virtually disappeared on the heels of seven losses in eight games. Miikka Kiprusoff suffered the setback while giving up three goals on 23 shots.