The Wild, whose 29 home wins were second only to Calgary's 30 last season, improved to 2-0 at home.
Wild coach Jacques Lemaire, who blasted his team's effort after they opened the season with a 1-0 win over Chicago, saw much more to his liking in game two.
"Our willingness to keep going and keep working, we got the puck from that, we got a good bounce, and that's how we got a couple breakaways," said Lemaire.
Defensemen Ron Hainsey and Adam Foote had the goals for the Blue Jackets, who opened the season with a home shutout of Anaheim on Friday, but led a late lead slip away against the Wild.
"I think early, the first 20 games, everyone knows how important points are, and how critical it is to get off to a good start," Columbus coach Ken Hitchcock said. "That's why I was disappointed for us. Back to back we had the game that we wanted but we made some errors and they ended up in our net."
Defensive lapses led to two of Minnesota's goals, when Bouchard and Belanger got behind the defense for unobstructed trips to the Columbus net.
"We capitalized on a couple turnovers by them and that was the difference in the game," said Rolston, who led the Wild with 31 goals last season. The three assists tied his career high. "I think we caught them on a change one time, and the other time we got a real nice break off a skate."
The Blue Jackets' special teams, which accounted for three of the team's four goals in their season-opening win, clicked again. Hainsey scored his second goal in two games with a shot from the left circle on the power play.
After Bouchard tied the game by tucking the puck past a sprawling Fredrik Norrena in the final minute of the first period, Foote scored short-handed in the second, blasting a puck off the goal post and past Minnesota goalie Niklas Backstrom.
Later Foote said later the overall effort wasn't enough.
"They just outskated us," he said. "They played at a playoff pace tonight and we didn't. We weren't ready for them."
Backstrom finished with 19 saves for Minnesota.
Norrena, making his first start, had 28 saves for Columbus.
Wes Walz, who centered Marian Gaborik and Pavol Demitra in Minnesota's season opener, missed Saturday's game after injuring his right knee in practice. ... Columbus center Michael Peca, who signed a free agent contract with the team in late August, did not make the trip to Minnesota. He has missed the first two games with back spasms, but is expected to play Wednesday when the Blue Jackets host Phoenix. ... Bouchard's goal was the 50th of his career, making him the seventh player in Wild history to score 50 goals with the team.
Copyright by STATS LLC and The Associated Press
Arena: Xcel Energy Center Location: Saint Paul, Minnesota
Referees: Michael McGeough, Brad Meier Linesmen: Derek Amell, Brad Lazarowich
Attendance: 18,568 (102.8% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Ron Hainsey (2)
(Power Play) Assists: Nikolay Zherdev, Jason Chimera
Pierre-Marc Bouchard (2)
Assists: Eric Belanger, Brian Rolston
Adam Foote (1)
(Shorthanded) Assists: Jiri Novotny, Nikolay Zherdev
Eric Belanger (1)
Assists: Brian Rolston, Keith Carney
Brent Burns (1)
Assists: Pierre-Marc Bouchard, Brian Rolston