Robert Bortuzzo also scored, Vladimir Tarasenko had an assist, and Tyler Pitlick had two assists for the Blues, who are 4-0 in the preseason.
Buchnevich, Bortuzzo and Tarasenko were each playing his first game of the preseason. Pitlick, who is in training camp on a professional tryout contract, has four assists in three preseason games.
Thomas Greiss made 23 saves on 25 shots in two periods before being replaced by Colten Ellis, who made 10 saves in the third.
Yegor Chinakhov scored twice, and Nolan Lalonde made nine saves in 29:34 for the Blue Jackets. Pavel Cajan allowed four goals on 12 shots in relief.
Chinakhov gave Columbus a 1-0 lead at 3:50 of the first period, scoring from the point on a delayed penalty. He then extended it to 2-0 at 11:07 of the second period when he skated down the left side and beat Greiss five-hole.
Buchnevich cut the lead to 2-1 at 12:19, scoring from the slot on the power play.
Bortuzzo scored 28 seconds later on a slap shot from the point to tie it 2-2.
Hugh McGing gave St. Louis a 3-2 lead at 18:40, scoring with a backhand as he crashed the net off a pass from below the goal line by Pitlick.
Niko Mikkola scored at 13:10 of the third period for the 4-2 final.
