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.
Ohio crash that killed two caught on camera [VIDEO]
Couple calls 9-1-1 over missing hash browns; assault McDonanld's employees