Scottie Upshall also scored for St. Louis (18-8-2), which outshot the Canadiens 30-25 and had the edge in play for most of the game.
Shea Weber scored twice and Jordie Benn also had a goal for Montreal (13-1-3-3), which ended a five-game winning streak and also saw goalie Carey Price lose for the first time in six games since returning from a lower-body injury.
Good work in the Montreal zone led to the Blues’ opening goal at 5:00 as Jaden Schwartz set up Schenn from behind the net for a one-timer to the top corner.
The Canadiens didn’t get their first shot on goal until after the 12-minute mark, but then it didn’t take long to score as Benn’s point shot through traffic got by Jake Allen at 15:28. Benn, who tied a career high with his fourth of the season, has six goals in 41 games for Montreal after scoring 11 in 302 games for Dallas.
The Blues owned the entire second period, but needed only a brief moment to score twice as Upshall finished a rush with Dmitrij Jaskin at 2:32 and Schenn took a feed at the Montreal blue line from Alex Pietrangelo and went in alone to beat Price at 2:39.