Vladimir Tarasenko scored twice, Buchnevich had a goal and an assist, and Jordan Binnington made 23 saves for St. Louis.
"I thought the first period was not bad," Blues coach Craig Berube said. "We passed up a lot of opportunities to get the puck to the net in my opinion, missed the net on some real good opportunities in the first. I think our game was pretty good. We had good energy. I thought we were on top of things for the most part. Second period, we got sloppy and let them back in the game."
Gustav Nyquist and Sean Kuraly scored, and Elvis Merzlikins made 20 saves in his season debut for Columbus (0-3-0), which was coming off a 5-2 loss to the Tampa Bay Lightning on Friday.
"There was lots of good stuff tonight, lots of it," Blue Jackets coach Brad Larsen said. "You think about the situation we're in, comparing it to last game, we played a heck of a game here tonight. Teams will force you into some situations. Unfortunately right now, we're making some really careless mistakes with the puck that's cost us, and every time we seem to make it, it's in the back of our net."