Fleury's second shutout of the season was the 73rd of his career, which is 12th all-time in the NHL.
Minnesota played without defensemen Jonas Brodin (upper-body injury) and Jon Merrill (illness).
"Great team effort," Fleury said. "We had some guys out on the [defense], but we have some depth back there. The guys blocked a lot of shots and let me see the puck."
Kirill Kaprizov and Brandon Duhaime scored in the first period for the Wild (32-21-5), who are 5-1-1 in their past seven games.
"That's kind of what we stressed, a big start, and we went out and played like it in the first period," Duhaime said.
Joonas Korpisalo made 23 saves for the Blue Jackets (18-35-5), who are 3-2-1 in their past six games.
"They don't give up much. There are a big body team, they're well coached, they're big on the wings," Columbus coach Brad Larsen said. "They've got solid [defensemen]. Their goaltender's good. They defend. They are a hard man-on-man [team] too, so if you're not getting inside and you're not beating your guys, it's going to be a long night.
"They're one of the top teams in their goals against for a reason. It's not by fluke; it's by design."