Armia gave the Canadiens a 1-0 lead at 6:12 of the first period, shooting past the outstretched pad of Fleury after Joel Edmundson's shot attempt deflected off the skate of Vegas forward William Carrier.
Toffoli made it 2-0 at 16:30. He fanned on a one-timer off a pass from Cole Caufield, but the puck managed to beat Fleury five-hole.
Toffoli has scored 10 points (five goals, five assists) during an eight-game point streak, which is one shy of tying Larry Robinson (1978) and Guy Lafleur (1977) for the longest in Canadiens playoff history.
"A little disappointed obviously with our first 10 minutes," Golden Knights coach Peter DeBoer said. "I think we should have been better. We had no excuse tonight. Unfortunately, you get to the final four, you spot a team two goals, you're playing with fire."
Vegas had chances to score early in the second period. Max Pacioretty hit the post on a partial breakaway at 3:22, and Alec Martinez took a one-timer from below the left circle at 5:17 which Price was able to get a piece of with his body.
Byron made it 3-0 at 17:45 of the second period with a backhand on a breakaway.
"We had lots of chances to score. The power play needs to score (0-for-2)," Stone said. "We had opportunities to claw our way back in the game, but you go down two after the first and then you get down 3-0, it's a tough hill to climb."
Pietrangelo cut it to 3-1 at 18:46 when his shot from the right point following a face-off win by Keegan Kolesar made it through traffic. He then got the Golden Knights to within 3-2 at 14:46 of the third period with a shot that went through the legs of Petry and under Price's glove.