Ryan Hartman and Joel Eriksson Ek scored, and Cam Talbot made 35 saves for the Wild, the No. 3 seed.
"We left Cam out to dry a little bit there -- a lot," Hartman said. "We gave them everything. We had no possession, no work ethic, no battle. We got away from our game, and we let them dictate. We gave them everything there."
Game 4 will be played here Saturday.
Hartman scored with a backdoor one-timer off a cross-ice pass from Kirill Kaprizov to give Minnesota a 1-0 lead 2:16 into the game. It was Kaprizov's first Stanley Cup Playoff point.
Eriksson Ek made it 2-0 at 8:30. After Fleury made the save on Mathew Dumba's shot from the right point, Wild forward Marcus Foligno got his stick on the puck in the slot, and Eriksson Ek gathered it and scored past the goalie's right pad.
"We played with energy and just going after them, making smart decisions on the lines and getting open, helping each other out, and we did that good in the first period," Eriksson Ek said.
Eriksson Ek scored again at 13:05, but Vegas challenged for offside, and video review showed Kevin Fiala entered the zone ahead of the puck at 12:52.
"Obviously when you get down by two, you always, you can get back in the game pretty quickly," Fleury said. "You get that first goal and it's 2-1, and there's still a lot of time to be played in the game. I thought that was a huge call by our coaches, and after that in the second and third, I thought we took over and played so well."