Jonatan Berggren and Robert Thomas scored for the Blues (17-18-8), who defeated the Vegas Golden Knights 4-3 here Friday.
Jacob Fowler made 17 saves for the Canadiens (22-13-6), whose seven-game point streak ended (5-0-2).
Berggren made it 1-0 at 10:48 of the first period. After a turnover by the Canadiens in their own end, Cam Fowler skated down the slot and found Berggren in the right face-off circle for a one-timer.
Thomas scored short-handed for a 2-0 lead at 10:13 of the second period, backhanding a loose puck at the left side of the net after starting the play by picking off a pass from Lane Hutson in the neutral zone.
The Blues killed off a 5-on-3 advantage that lasted 1:37 for the Canadiens in the second, with Binnington making six saves in that sequence. St. Louis was 4-for-4 on the penalty kill.