Jarret Stoll and Nino Niederreiter scored, and goaltender Devan Dubnyk made 18 saves to help the Wild extend their season-high winning streak to six games.
"We're playing a team game. We're playing a fast, tight-checking style of a game, and that's how we need to play," Stoll said. "We can suffocate teams with our speed and checking ability and that's what we did here tonight. We can do that against any team in this league, and that's how you win in the playoffs, you win 2-1, 3-2, 1-0 by checking well, playing on the right side of the puck, and getting opportunities from that."
Marian Hossa scored for the Blackhawks (44-26-7), who were without their top two defensemen for most of the game. Goaltender Scott Darling made 14 saves.
Chicago, which clinched its eighth straight playoff berth Sunday, is six points behind the Dallas Stars and Blues for first place in the Central Division and four ahead of the fourth-place Predators. Dallas defeated Nashville 5-2 on Tuesday.
"Even if we would've won tonight, we wouldn't be satisfied going 1-4 [against Minnesota]," Blackhawks captain Jonathan Toews said. "Obviously, it adds insult to injury to lose this one tonight. There were a couple that we really didn't play well and didn't really deserve to win. I think tonight was an improvement, and obviously the score doesn't look that way. It's not fun to look back and have a record like that against a team in your division, especially a team like Minnesota. It's not something we're happy about."