Sammy Blais scored in his first game back with the Blues, Calle Rosen had two goals, and Buchnevich had three assists for St. Louis (24-25-3), which ended a five-game losing streak in its first game since Jan. 30. Jordan Binnington made 23 saves.
"We weren't playing very quick in the first period, a little methodical and slow," Blues coach Craig Berube said. "Better as it went along, better second, better third. The third goal is a tough one, then we took a penalty. Our penalty kill wasn't sharp tonight I don't think. We shouldn't have given up either goal. The tying goal, 6-on-5, we just didn't return hard enough to the middle of the ice.
"I liked a lot of things in the game, especially the second and the third. I thought we did some real good things offensively, and I liked our forecheck a lot tonight."
Clayton Keller had two goals and two assists, Nick Schmaltz had a goal and three assists, and Juuso Valimaki had four assists for the Coyotes (17-28-8), who were coming off a 4-3 overtime loss to the Chicago Blackhawks on Friday. Vejmelka made 31 saves.
Arizona scratched defenseman Jakob Chychrun before the game due to trade-related reasons.
"We have a job to do," Coyotes coach Andre Tourigny said. "'Chych' is a great guy, but there is a situation there that concerns him, our GM, our organization, obviously, and his agent. It's their job to deal with it, not my job."