Ryan Reaves and Max Pacioretty scored for the Golden Knights (39-27-5), who are 7-1-0 in their past eight games. Vegas is third in the Pacific Division, 11 points behind the San Jose Sharks.
Fleury has allowed five goals in winning his past six starts and leads the NHL with 35 victories.
"They've got some talented players," Fleury said. "It's fun. It's fun when it doesn't go in, right?"
WATCH: [All Golden Knights vs. Stars highlights]
Roope Hintz scored, and Anton Khudobin made 35 saves for the Stars (37-29-5), who are 6-2-0 in their past eight games. Dallas is tied with the St. Louis Blues for third in the Central Division, six points behind the second-place Nashville Predators.
"It was a playoff-style game, but we've been going through that since the break," Stars coach Jim Montgomery said. "It's been getting more and more intense. We're handling that part. The mental part has been impressive."
Reaves scored for the first time since Jan. 6 to end a 25-game goal drought at 2:37 of the third period on a rebound in the crease following a shot by Pierre-Edouard Bellemare to put Vegas ahead 2-1.
"[Bellemare] just got a good shot through, the goalie made a save, and [Bellemare] tied up the guy in front, and then it trickled to me," Reaves said. "These games and then going into the [Stanley Cup] Playoffs, they're going to be tight matches."