The Wild (12-7-1) lost in regulation for the first time since Feb. 16, a 4-0 loss to the Los Angeles Kings. Marcus Foligno scored his third goal in two games, and Cam Talbot made 23 saves.
"Not to get goals tonight was frustrating," Minnesota coach Dean Evason said. "It seemed like every opportunity they got it was in our net. Every opportunity that we got, Fleury seemed to be there, or we didn't finish. That was frustrating."
The Golden Knights took a 1-0 lead at 2:03 of the first period when Tuch received a cross-ice, backhand pass from Cody Glass along the boards and scored glove side.
Tuch, selected No. 18 by the Wild in the 2014 NHL Draft, was traded from Minnesota as part of Vegas selecting forward Erik Haula in the 2017 NHL Expansion Draft.
"It's been the same since Year One. Whenever we play those other teams, we have that chip on our shoulder," Tuch said. "I like playing against the Wild. It's been a lot of fun beating them, that's for sure."