The Wild killed off a penalty for the final 1:56 of overtime, then Kirill Kaprizov scored the only goal of the shootout.
Yakov Trenin also scored for the Wild (30-14-10), who are 4-1-1 in their past six games. Wallstedt made 29 saves.
“I thought in the first period they were the better team,” Minnesota coach John Hynes said. “I thought they were quicker, faster, harder on pucks. I think I would say that the readiness to play, I thought they had a really good first, I thought we battled ourselves back a little bit better in the second, but then in the third, I thought we really got to the game that we needed to get to.
“But what I really like is that we did not have a good start to the game, but it wasn’t that we just faded into the night. We held serve. ‘Wally’ made some really big saves for us. I really liked his composure and battle level throughout the game, and as it went on. And I particularly like our group, our team’s response that we dug in when it wasn’t an easy night, but we found a way to win. And that’s important.”
Teuvo Teravainen, Ryan Donato and Ilya Mikheyev scored for the Blackhawks (21-23-9) who have lost three straight (0-1-2). Spencer Knight made 20 saves.
“I mean, it’s 3-0 lead. A little bit unfortunate,” Chicago coach Jeff Blashill said. “Yet, at the end of the night, when you take the emotion out of it, which is obviously we’re frustrated, you know, the chances we had were 23-14 us, you’re going to win that game 98 percent of the time. We just didn’t win tonight. But I think the thing you have to do is, I thought, that’s the best we’ve played in a while to be honest with you.
“We can’t feel sorry for ourselves because we ended up giving up a late lead and lost in the shootout, we’ve got to learn from it and be ready to play similar on Thursday.”