Fiala made it 1-0 with a wrist shot on a 2-on-1 at 10:51 of the first period.
"We have to stay on, aggressive," Fiala said. "If it's [a] 1-0 game, we have to go for the next one. I feel this league is too good. If we sit back and just try to play defense, I feel like it's not going to go well.
"I feel tonight we did a good job. [Kahkonen] again, not just tonight, he's [been] unbelievable all season long."
Brodin was awarded an empty-net goal for the 2-0 final when he was slashed by Jonathan Marchessault.
"I think tonight they defended well, capitalized early in the game and we just couldn't get it back," Fleury said. "Close game all night long."
NOTES: Kahkonen tied Washington Capitals goalie Vitek Vanecek for the most wins by a rookie this season with 10. Among rookies in Wild history, he extended the longest winning streak and has the third-most wins in a season (Darcy Kuemper, 12, 2013-14; Josh Harding, 11, 2007-08). … Minnesota was 0-for-2 on the power play, is 0-for-19 in its past eight games and 5-for-74 (6.8 percent) this season. … Fleury had won five straight starts. … It was the second time the Golden Knights have been shut out in 22 games this season. They had scored four or more goals in each of their previous four games.