Jordan Binnington made 25 saves and earned his 100th NHL win for the Blues (13-15-1), who won for only the second time in eight games (2-5-1). St. Louis played the second of a back to back after losing 3-2 in overtime against the Colorado Avalanche on Sunday.
"Tough game," Blues coach Craig Berube said. "It's a heavy game, we knew that. It's always a heavy game with them. They're a big team. It was a good hockey game, battled, competed, heavy game all around."
Saros made 23 saves for the Predators (12-11-3), who lost their third straight (0-2-1). Nashville hosts the Edmonton Oilers on Tuesday.
"Too bad we couldn't win, but I think we could build something from that game," Saros said. "It was pretty tight, even the whole game."
Before the goal developed, Schenn had broken his stick after receiving a pass from Kyrou in his zone. He immediately tried to make the bench aware he had a broken stick, and Binnington came out to play the puck so Schenn wouldn't play it with a broken stick and risk a minor penalty.
Schenn got a new stick after assistant coach Steve Ott yelled from the bench.
"He's trying to let everybody know, but I couldn't hear him," Berube said of Schenn, who lost his voice during the game. "We saw that his stick was broke. [Ott] yells a lot louder than I do."
Each penalty kill unit held the game scoreless through two periods. St. Louis was 4-for-4 on the kill, and the Predators were 3-for-3.