Varlamov has given up a lone goal in each of his first two games, his other victory having come in a 6-1 decision over Anaheim.
Colorado scored in each period to leave the Predators with their second loss in two games.
P.A. Parenteau opened the scoring with 1:10 left in the first period and closed it with an empty-net tally with 1:12 remaining in the third.
Patrick Bordeleau produced Colorado's second period goal, after which Nashville cut its deficit to one on a score by Paul Gaustad.
Pekka Rinne was beaten twice on 35 shots to suffer the loss.
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