Brandon Saad and Robert Thomas each had a goal and an assist, and Joel Hofer made 30 saves for St. Louis (5-4-1), who have won two straight, including 4-1 against the New Jersey Devils on Friday.
"Just feels good as a team," Kyrou said. "We got back-to-back wins here. Energy's good right now."
Brendan Gallagher had a goal and an assist, and Sam Montembeault made 29 saves for the Canadiens (5-4-2), who went 0-2-1 on a three-game road trip.
"Pretty sloppy from us," Montreal captain Nick Suzuki said. "I thought we'd respond better after Arizona (a 3-2 loss on Thursday). It was the same things happening again. We need to clean things up."
Kyrou gave St. Louis a 1-0 lead 1:24 into the first period, cutting to the slot and taking a pass from Schenn from the left corner after Schenn missed a breakaway chance.
"He's another guy, too, where the stat sheet, what did he have, two or three points coming into this game?" Schenn said. "He had breakaways and 2-on-1s and stuff he wasn't scoring on. He's an opportunistic guy. Most importantly, I think his work ethic's where it needs to be right now. He's playing hard at both ends. He's backchecking and he's winning his battles. It was nice for him to get one, too."