Quinn Hughes had a goal and two assists, and Jesper Wallstedt made 23 saves for the Wild (12-3-3), who have won three in a row and are 6-0-1 in their past seven games.
Macklin Celebrini scored, and Yaroslav Askarov made 25 saves for the Sharks (7-10-1), who have lost four in a row and six of seven.
The loss also came two days after San Jose held a players-only meeting following a 7-2 loss at the Los Angeles Kings on Wednesday.
Kaprizov put the Wild up 1-0 during a 5-on-3 power play at 7:55 of the first period. He scored five-hole with a one-timer from the right circle off a cross-ice pass from Hughes for his League-leading 16th goal of the season.
Celebrini tied the game 1-1 at 12:11 of the second period when he redirected Dmitry Orlov’s shot above the blocker of Wallstedt.
Maxim Shabanov responded with another power-play goal to put the Wild back in front 2-1 at 14:15. He positioned himself down near the left post and tapped in a backdoor pass from Kaprizov.
Hughes increased the lead to 3-1 at 6:54 of the third period. He shook off Celebrini in the right circle, skated above the left circle, and roofed a wrist shot past the blocker of Askarov.
Zach Bogosian made it 4-1 with his first goal of the season at 13:58. He skated into a rebound along the right boards and ripped a slap shot that found the far corner of the net.
