The Avalanche, who beat Dallas on Thursday in their preseason opener, got goals from Chris Stewart and Matt Duchene, the third overall pick from the 2009 draft.
Goalie Ty Conklin, signed as a free agent by the Blues in the offseason, made his debut with the team and stopped 21 shots through two periods before being replaced by Jake Allen. Colorado's Tyler Weiman played the entire game and stopped 30 shots.
Drazenovic scored 9:39 into the first period on a one-timer from the left circle and Kariya, who skated in his first game Tuesday in nearly a year following surgeries on both hips, notched his second goal in as many games 12:26 into the opening period.
Steen was given credit for the Blues' third goal of the period at 15:02 when Colorado's Wojtek Wolski inadvertently backhanded the puck into his own net trying to clear it around the boards.
The Blues led 4-0 on Oshie's goal at 4:18 of the second before Stewart got the Avalanche on the board with 1:08 remaining in the period.