Zuccarello gave the Wild a 2-1 lead at 8:01 after Kaprizov fed a spinning, no-look pass across the net mouth.
"Yeah, I saw [Zuccarello]," Kaprizov said. "He jumped in the middle, and we are just trying to make some plays."
The Wild had two apparent goals waved off for offsides following San Jose challenges in the second period, first by Joel Eriksson Ek at 1:01 and then by Ryan Hartman at 10:37.
"[The video coaches] are super prepared for every call. They look at it in depth," Warsofsky said. "They look at every call that's made in the National Hockey League, goal scored [or] not called back. They do a lot of preparation through the summer."
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.