Paul Stastny, Jori Lehtera and Patrik Berglund also scored for the Blues, who reached 100 points for the third time in four seasons without top forwards Vladimir Tarasenko and Alexander Steen. St. Louis is in second place in the Central Division with 101 points, two behind Nashville, with five games to go.
The Blues ended a 10-game first-period goal drought when Schwartz scored his 25th on a backhander at 1:16. They entered the night just 1-3-2 in their previous six games and needing a victory or a Los Angeles regulation loss to earn their fourth consecutive playoff berth.
Sean Monahan scored his 30th goal for Calgary.