Dylan Holloway had a goal and two assists while Pavel Buchnevich also scored for St. Louis (11-12-7), which beat the Senators 2-1 in Ottawa on Saturday.
Jordan Binnington stopped 23 shots.
Cole Caufield extended his point streak to 11 games with a goal for Montreal (15-10-3), matching a career-best. Noah Dobson had a goal and an assist, and Lane Hutson also scored as a two-game winning streak came to an end.
Jakub Dobes made 14 saves in his second start in 24 hours after backstopping the Canadiens to a 2-1 shootout win in Toronto on Saturday.
Sam Montembeault, the expected starter Sunday, was ruled out two hours before puck drop because heâ€s sick, the team said. The Canadiens recalled Kaapo Kahkonen from the AHLâ€s Laval Rocket to back up Dobes.
Schenn opened the scoring on the power play, firing a shot in a gaping net after a deflection from Cam Fowlerâ€s point shot landed on his stick at 8:57 in the first period.
Hutson evened the score with a highlight-reel deke to the backhand at 12:20 in the first, and Caufield buried his 16th of the season with 57 seconds remaining in the period.
The Blues scored twice 65 seconds into the second — and 39 seconds apart — to take a sudden 3-2 lead. Holloway finished off a St. Louis rush through Montrealâ€s defence, then Robert Thomas set up a wide-open Buchnevich before most fans had returned to their seats.
Schennâ€s second of the night, off a feed from Holloway on a 2-on-1, made it 4-2 with 9:36 remaining.
Dobson pulled one back with the extra attacker with 3:45 left, but St. Louis hung on for the win.
Blues: Capitalized on their opportunities when the Canadiens left Holloway and Buchnevich alone in front during an otherwise tight-checking game.
Canadiens: Drove the play all night and limited the number of St. Louis chances, but went 0-for-2 on the power play and only registered eight shots in the third period.
Hutson, last yearâ€s Calder Trophy winner, jumped in from the point, received a pass from Zack Bolduc and dangled around Binnington to the backhand for his fifth of the season. The Canadiens acquired Bolduc from St. Louis for defenceman Logan Mailloux on July 1.
Holloway and Buchnevich scored the fastest two goals to begin a period for the Blues since Jan. 30, 2021.
Blues: Host the Boston Bruins on Tuesday.
Canadiens: Host the Tampa Bay Lightning on Tuesday.
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