Golden Knights goalie Robin Lehner was expected to start but was a late scratch and is day to day because of an upper-body injury sustained at the morning skate. Oscar Dansk backed up Fleury.
Fleury made 12 saves on 12 shots in the first period, when Vegas had four.
"Unfortunate to waste an effort like that. He was our best player," Golden Knights coach Peter DeBoer said. "Considering the circumstances, he got the call to go in late tonight, it was a great effort by him. I know the guys feel like they let him down tonight."
Anaheim outshot Vegas 21-11 in the first and second periods.
Fleury reached back to make the save with his left arm on Isac Lundestrom cutting across the crease from left to right at 9:53 of the second period, then tossed the puck out of the crease.
Fleury said he was surprised he made the save.
"I knew I was kind of [in trouble] on that one," Fleury said. "I tried to get back for the shot, and he came across, went around my poke check, and hopefully scared him a little bit. I threw my arm back there, tried to cover a little something, and got a little lucky."