Rookie Kirill Kaprizov scored his first Stanley Cup Playoff goal, and Cam Talbot made 38 saves for the Wild, the No. 3 seed in the Honda West Division.
"The guys believed," Minnesota coach Dean Evason said. "The looks we were getting, the goals we scored tonight, that's what we've talked about. We just have to believe in that. The guys did persevere, and it's something that's inside them. It's a standard they have set for themselves that they don't panic, and we didn't do that tonight."
Mark Stone and Alec Martinez scored for the Golden Knights, the No. 2 seed, who won the previous three games. Marc-Andre Fleury made 10 saves.
"I thought we played a pretty solid game," Stone said. "We had lots of chances and could've easily tied that game up, or could've easily been ahead. … If we capitalize on a few chances, I think we're sitting here with a different outcome."
Game 6 of the best-of-7 series is at Minnesota on Wednesday.
Stone gave the Golden Knights a 1-0 lead at 8:14 of the first period with a shot from the left face-off circle.
Kaprizov tied it 1-1 at 9:06 with a one-timer off a pass from Mats Zuccarello that ended a 120:34 goal drought for Minnesota, which lost 4-0 in Game 4 at home Saturday.