It was Colorado's fourth win in a row and its ninth in 10 games. The Avalanche have rebounded from a struggling stretch in which they lost 11 times in 14 outings leading up to the Thanksgiving holiday.
Varlamov is in his first season with the Avalanche, having played with Washington during his first three years in the NHL. He has six career shutouts in 87 appearances.
David Jones opened the scoring with 7:03 to go in the first period and Colorado boosted its lead in the second on goals from T.J. Galiardi and David Van der Gulik. It was the first goal of the season for Van der Gulik and only his second in 22 NHL games spanning three seasons.
Chuck Kobasew added a goal with 1:56 left in the contest.
Corey Crawford stopped 18-of-22 shots for the Blackhawks, losers of three in a row.