Carl Soderberg added an empty-net goal with 22 seconds remaining to seal Colorado's fifth win in seven games.
Varlamov stopped the first 36 shots until Vladimir Tarasenko spoiled his shutout bid with a power-play goal with 7:05 remaining. It was Tarasenko's team-high 18th of the season.
Jake Allen, starting for the second straight day, had 15 saves for the Blues, who fell to 2-4-1 in December.
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