Patrick Berglund scored the other goal for the Blues on a power play early in the second period. St. Louis outshot the visitors 34-18 and were 2-for-5 on power plays.
Elliott, who had been pulled in the opener of the home-on-home series with the Avalanche, lost his bid for a shutout at 15:01 of the second period when Cody McLeod scored the lone Colorado goal on assists by Paul Stastny and Greg Zanon.
Semyon Varmalov made 31 saves for the Avalanche, who lost for the 16th time in their last 17 road games.
Notable deaths of 2014 [PHOTOS]