Jordan Kyrou pushed the lead to 3-1 at 13:12 on a breakaway.
The Blues outshot the Blue Jackets 17-8 in the second and had the first 10 shots.
"I liked the first, and for about 14 minutes there [in the second] we couldn't stop anything, we couldn't gather ourselves, and the last six [minutes] we were fine, kind of caught ourselves," Blue Jackets coach Brad Larsen said. "In the third, we were fine and then a couple mistakes and that's it.
"Good teams do that. They're a good hockey team, a big, heavy team. They got rolling there and we didn't have an answer for them."
Boqvist's one-timer from the slot on a power play at 1:03 of the third period brought the Blue Jackets within 3-2.
Justin Faulk took a pass from Robert Thomas in the slot and beat Korpisalo with a wrist shot at 5:42 to make it 4-2.
Buchnevich converted another Thomas pass through the crease at 10:30 to extend the lead to 5-2, and Barbashev made it 6-2 at 12:40.
"I feel like the more we play in the line, the more he plays for the Blues, he will find out the way we play hockey," Tarasenko said of Buchnevich, who was acquired in a trade with the New York Rangers on July 23. "It's a little bit different. And he's doing really well, it's nice to play with him.
"And Robert, I think we start to understand each other better on the ice. It's always easy to play when you know what the guy next to you will do in the next second, so you don't need to think about it."
Boqvist scored at 17:46, a wrister from the right circle, for the 6-3 final.
NOTES: Boqvist has five points (three goals, two assists) in a three-game point streak. ... Blues forward David Perron missed the game with, an upper-body injury sustained in the first period of a 3-2 overtime loss at the Chicago Blackhawks on Friday. ... Buchnevich has 13 points (six goals, seven assists) the past 11 games, including six points (four goals, two assists) in a three-game point streak. ... Tarasenko has 21 points (10 goals, 11 assists) in 16 games against the Blue Jackets. ... Thomas, who had two assists, has 12 points (one goal, 11 assists) the past 10 games.