Robertson scored with a wrist shot off a pass Thomas Harley.
Matej Blumel, Kyle McDonald and Matthew Seminoff scored, and Evgenii Dadonov, Harley and Lian Bichsel each had two assists for the Stars. Matt Murray allowed three goals on seven shots before being replaced by Remi Poirier, who stopped all eight shots he faced.
Brayden Schenn scored two goals for the Blues. Jordan Binnington made 12 saves before being replaced at the start of the third period by Colten Ellis, who allowed three goals on 16 shots.
Schenn gave St. Louis a 1-0 lead on a rebound at 1:04 of the first period, but Blumel tied it 1-1 on a breakaway 22 seconds later.
Schenn put the Blues back in front 2-1 at 4:19 on a deflection.
Zachary Bolduc extended the lead to 3-1 at 13:07 with a one-timer from the right face-off circle.
McDonald cut it to 3-2 at 2:46 of the third period, and Seminoff tied it 3-3 on a rebound at 11:40.
Jordan Kyrou missed a penalty shot with eight seconds remaining in the third for the Blues.
