Kaprizov moved into second in the NHL with 24 points, behind Colorado’s Nathan MacKinnon (25 points).
Matt Boldy scored twice for the Wild (9-2-2), who have won four of five. Zach Bogosian, Mats Zuccarello, and Jonas Brodin also scored, and Marc-Andre Fleury made 24 saves.
Macklin Celebrini scored two goals and Vitek Vanecek made 26 saves for the Sharks (4-9-2).
Celebrini, the No. 1 pick of the 2024 NHL Draft, was playing his second game after missing 12 games when he re-aggravated a hip injury in the season opener. He has four points and three goals in three games.
Bogosian sent a wrist shot from the right point that deflected off San Jose’s Will Smith’s skate and past Vanecek’s blocker to give the Wild a 1-0 lead 2:22 into the first period.
Joel Eriksson Ek’s score at 1:01 of the second period was waved off for offsides following a San Jose challenge.
Celebrini took a pass from Mikael Granlund in the slot and shoveled the puck into an open net to make it a 1-1 game at 4:36 of the second period.
Zuccarello gave the Wild a 2-1 lead at 8:01 after Kaprizov fed a spinning, no-look pass across the net mouth.
The Sharks again won an offside challenge after Ryan Hartman’s deflection at 10:37 was waved off.
Boldy gave the Wild a 3-1 lead with a power-play goal at 13:26 with a shot over Vanecek’s glove from the right circle.
Brodin walked the blue line before taking a slap shot that got past Vanecek’s glove at 6:02 of the third period to give the Wild a 4-1 lead.
Celebrini beat Fleury over the glove with a wrist shot from the high slot at 16:08 to make it a 4-2 game.
Boldy skated the puck into the net for the empty-net goal at 18:25 to make the 5-2 final.