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.
“I thought we worked harder,” coach Ryan Warsofsky said. “I thought we got above quicker, we reloaded quicker without the puck. It was a pretty even game up until that point."
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.
"We just try to play smart," Kaprizov said of his line. "Sometimes we go D-zone, too, and just try to put puck in offensive zone and just play smart and play good in the line."
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.