"Everyone is still working on getting the system down, but tonight is the best I've seen so far this preseason," Blue Jackets coach Scott Arniel said.
Antti Miettinen and Matt Cullen scored for the Wild (0-4-2), which finished a disappointing 13th in the Western Conference last year.
"It seems like we're waiting and I don't know what we're waiting for," Wild coach Todd Richards said. "It can't be something where we say, 'OK, let's go now.' By then, it might be too late."
Minnesota was scheduled to leave after the game for Helsinki, Finland, where it will play an exhibition against Tampere Ilves on Monday before opening the regular season on Thursday against Carolina.
After Miettinen cut the Blue Jackets' lead to 2-1 in the second period, Pahlsson slipped a shot past goalie Niklas Backstrom and Voracek scored 1:01 later to put Columbus back in control.
"After the other team scores, your psyche might be to get back on your heels," Arniel said. "We did a great job of getting up and getting after it tonight. That's the kind of mentality you need to have."
Wild defenseman Brent Burns left in the third period after tweaking his back. Richards said the injury didn't appear to be serious.
Cullen's goal was his first at home after signing with the Wild in the offseason.
"Fortunately, none of these count, but we need to get some things in order," Cullen said.
Blue Jackets captain Rick Nash played after missing Tuesday's game with a charley horse.