Kaprizov skated down the slot for a wrist shot 45 seconds into overtime.
Kaprizov also had an assist, Mats Zuccarello had two goals and an assist, and Quinn Hughes had three assists for the Wild (29-14-9), who have won three of their past four. Filip Gustavsson made 31 saves.
Lucas Raymond scored two goals and James van Riemsdyk also scored for the Red Wings (31-16-5), who played in their third straight overtime game. Cam Talbot made 35 saves for Detroit, which is 7-1-1 in its past nine games.
Raymond made it 1-0, 32 seconds into the power play at 4:39 of the first period with a snipe to the corner from the right dot.
Kaprizov tied it 1-1 at 17:19 on the power play with a snap shot that bounced off the inside of Talbot’s pads.
Raymond put Detroit ahead 2-1 at 16:22 of the second period after Marco Kasper interrupted a Marcus Johansson clearing attempt and the puck found Raymond in the slot for the snap shot.
Zuccarello tied it 2-2 37 seconds into the third period, scoring off the rebound after Talbot made a glove save on Hughes’ point shot but couldn’t hold on to the puck.
Van Riemsdyk brought it to 3-2 at 5:36 with a backhand redirect of Emmitt Finnie’s pass, but Zuccarello responded 35 seconds later at 6:11 with another rebound goal to make it 3-3.
