Varlamov replaced Jean-Sebastien Giguere in goal after Giguere suffered a groin injury late in the first period.
Giguere allowed a goal to David Booth 13 seconds into the game and Colorado tied it in the second on a wrist shot from Erik Johnson.
Roberto Luongo got the win by making 29 saves. The Canucks boosted their lead over Calgary in the Northwest Division to 16 points.
2014: NFL Cheerleaders [PHOTOS]
Michael Sam cut from the Dallas Cowboys