Fleury, who made 14 saves, tied Ed Belfour with his 484th win, which is five behind Roberto Luongo for third. Fleury also tied Patrick Roy for 15th in League history with his 66th shutout.
"With Patrick, he was one of my idols growing up. Loved watching him and obviously I have a lot of respect for him," Fleury said. "It's humbling to be up there with him."
Fleury's win was his first in four starts for Vegas, which has scored five goals in those games.
"The past few games had been hard. Couldn't get a win. Took a while," Fleury said. "Maybe we weren't scoring much as we used to, but I didn't make the key saves to keep us in and get us those wins. Tonight was a different style game, a little harder mentality, but it was nice to get the win in the end."
Tomas Nosek scored the lone goal for the Golden Knights (27-11-2), who swept the two-game set and have won three of their past four.