Patrik Berglund had two goals, including an empty-netter to seal it for the Blues. They tied idle Nashville for third place in the Central Division with 83 points, and St. Louis holds the tiebreaker by virtue of more regulation and overtime wins.
The Blues have won eight of 11 overall and 14 of their last 20 road games.
Jake Allen finished with 26 saves for St. Louis, which played most of the game without center Paul Stastny after he was hit on the foot by a shot in the first period.
John Mitchell had a goal and an assist, Mark Barberio also scored and Calvin Pickard made 25 saves for Colorado, which has lost three straight. The Avalanche, last in the NHL in points with 43, fell to 11-23-2 at home. Their 11 home wins are the fewest in the league.
The game was tied 1-all after two periods before Paajarvi deflected Ivan Barbashev's shot past Pickard at 5:05 of the third. Schwartz made it a two-goal lead at 8:44 with his 15th of the season.
Barberio got Colorado within one with his second of the season at 14:50. Pickard came off for an extra skater in the final two minutes and Berglund scored his 21st goal into the empty net at 19:12.
Mitchell's first goal in 19 games and third of the season at 5:32 of the first gave Colorado a 1-0 lead. The Avalanche had the first eight shots of the second but it was the Blues who got the only goal of the period when Berglund scored at 16:50.
Blues RW Dmitrj Jaskin was out of the lineup for the fourth straight game with an upper-body injury. He has started skating but there is no timetable for his return. ... Avalanche D Erik Johnson celebrated his 28th birthday. ... Blues RW Vladimir Tarasenko has seven points (six goals, one assist) in his past eight games. D Alex Pietrangelo has nine points (two goals, seven assists) in his last 12 games.