Jonathan Marchessault tied the game 2-2 with 1:02 remaining in the third period on a slap shot from the left face-off circle.
"I think over a long season, you have to win all kinds of different ways," Vegas coach Peter DeBoer said. "You're going to show up tired, you're going to show up off your game. You've got to get hot in different areas. Tonight, it was goaltending, and we hung around and found a way at the end."
Laurent Brossoit made 32 saves in his first start for the Golden Knights (3-4-0), who won 3-1 at the Colorado Avalanche on Tuesday. Shea Theodore had a goal and an assist.
"I thought our guys did a great job of weathering the storm the first period," Brossoit said. "Getting the plane legs, the travel legs, out of us and making smart choices. Chipping pucks out, as cliché as that sounds."