Varlamov tied his career high with his sixth victory in a row and improved to 7-1 in December.
Tyson Barrie had a goal and an assist, and Blake Comeau and Nick Holden also scored for the Avalanche. Colorado (17-16-1) is above .500 for the first time this season.
It is the longest winning streak for the Avalanche since they won six straight from March 25 to April 5, 2014.
Andrej Sekera scored for the Oilers, who have lost three in a row following a six-game winning streak.
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