Quick made 31 saves for his 375th win, moving past John Vanbiesbrouck (374). Ryan Miller is first with 391.
Quick is 5-1-0 since being acquired from the Columbus Blue Jackets on March 2.
"You think about some of the guys that are at the top of that list and being in a category with them, it's just an honor," Quick said. "And obviously you think about all the guys that kind of helped me get a bunch of those wins and the work they put in, and you are just very appreciative of everything."
Four players scored, and William Karlsson had two assists for the Golden Knights (44-21-6), who have won six of their past seven games and moved two points ahead of the Los Angeles Kings for first place in the Pacific Division.
"Would I call it our best game? No, maybe not," Vegas defenseman Alex Pietrangelo said. "Was it perfect? No. It usually isn't on the road, but we found a way to win it, and that's been kind of the recipe for us. We'd love to play the perfect game, but we're just finding ways to win and having contributions up and down the lineup."