Joel Eriksson Ek and Maxim Shabanov scored, and Quinn Hughes had two assists for the Wild (9-3-2), who have won three straight and finished their five-game road trip 3-1-1. Jesper Wallstedt made 26 saves.
Logan Cooley scored, and Karel Vejmelka made 27 saves for the Mammoth (8-5-0), who have lost three of their past five games.
Ryan Hartman appeared to put the Wild up 1-0 with a power-play goal at 7:21 of the second period, but the goal was disallowed after video review confirmed Hartman kicked the puck into the net.
Eriksson Ek opened the scoring with a power-play goal at 15:04, putting a one-timer from the left face-off circle off the right post and in to give the Wild a 1-0 lead.
Kaprizov scored a power-play goal just 48 seconds into the third period, whipping the puck into an open net from the right circle off a pass from Matt Boldy to extend it to 2-0.
Shabanov picked up a loose puck in the slot and beat Vejmelka to the blocker side to make it 3-0 at 11:44.
Cooley got the Mammoth on the board at 18:39. Mikhail Sergachev's shot from the point was deflected by Nick Schmaltz, and the puck bounced off the left post in the crease to Cooley, who put it home for the 3-1 final.
