After spotting the Blues a 1-0 lead, Liles found the net 5:05 into the period and again at 12:55, putting the Avs ahead for good.
Liles added an assist while Paul Stastny scored a goal and an assist for Colorado, which won for the third time in five games.
St. Louis got a goal and an assist each from Alex Steen and Carlo Colaiacovo and Brad Boyes also scored in the Blues' fourth straight setback.
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