Varlamov improved to 3-1 in his last four starts and 3-0-0 lifetime against Minnesota with his eighth career shutout as the Avalanche pulled to within one point of San Jose for the final Western Conference playoff seed.
Jamie McGinn netted both goals in the first period, while Peter Mueller and Stefan Elliott each assisted on both tallies for Colorado, which snapped a two-game skid.
Matt Hackett turned aside 34-of-36 shots as Minnesota dropped to 2-6-1 in its last nine home games.
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Penelope Cruz named 2013's 'Best Body' by Fitness magazine