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 Schenn pass 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 back-checking and he's winning his battles. It was nice for him to get one too."