Kaprizov scored on a wrist shot from the left face-off circle after Chicago forward Ilya Mikheyev was called for interference against Joel Eriksson Ek at 53 seconds.
Matt Boldy had a goal and two assists, and Brock Faber had a goal and an assist for the Wild (13-7-4), who extended their point streak to nine games (8-0-1). Jonas Brodin had two assists, and Filip Gustavsson made 34 saves.
Connor Bedard had a goal and an assist, and Artyom Levshunov scored his first NHL goal for the Blackhawks (10-8-5), who have lost four in a row. Spencer Knight made 20 saves.
Levshunov, a 20-year-old defenseman, was the No. 2 pick in the 2024 NHL Draft.
Jason Dickinson put Chicago ahead 1-0 at 5:41 of the second period, scoring from the slot after the puck came off the stick of the Wild’s Yakov Trenin along the left-wing boards.
Bedard extended it to 2-0 at 12:08. Tyler Bertuzzi carried the puck into the offensive zone and passed across ice to Sam Rinzel, who quickly fed it to Bedard in front of the net.
Bertuzzi appeared to score at 16:07, but after a coach’s challenge by the Wild, the Blackhawks were ruled to have been offside entering the zone and the goal was overturned.
Faber cut it to 2-1 at 19:46 when his wrist shot from inside the right point deflected off Bertuzzi, fluttered over Knight’s right shoulder and went in off the post.
Nico Sturm tied it 2-2 at 2:17 of the third period, tipping in a shot from Brodin.
Levshunov put the Blackhawks back ahead 3-2 at 5:31. Bedard passed cross-ice to Levshunov, who skated through the right circle and scored on a backhander.
Boldy then tied it 3-3 at 10:35, scoring from in front after taking a backhand pass by Brodin from behind the net.
Wild forward Marcus Foligno did not play in the third period after sustaining an apparent injury late in the second.