Mark Stone scored a hat trick, Jack Eichel and Shea Theodore each had three assists, and Reilly Smith had a goal and an assist for Vegas. Adin Hill made 32 saves.
The Golden Knights had seven goal-scorers and 15 players with at least one point.
"Depth all year," Vegas defenseman Alex Pietrangelo said. "We just used our depth to overwhelm people."
Sam Reinhart and Sam Bennett each had a goal and an assist, and Sergei Bobrovsky made 23 saves for the Panthers.
"Appropriate congratulations to Vegas, they earned it," Florida coach Paul Maurice said. "They were outstanding. We didn't have an answer for them."
The Panthers played without forward Matthew Tkachuk, their leading scorer in the playoffs (24 points; 11 goals, 13 assists), who broke his sternum in Game 3 but played through the injury in Game 4.
Maurice credited Tkachuk with being a smart enough player to make an impact in Game 4, but the pain was too great for him to keep going.
"He didn't dress himself for the game," Maurice said. "Somebody helped him get his gear on. Somebody tied his skates. Somebody put his sweater on for him. But the next day when he came in he was in significant pain, so it wasn't really a question of whether he'd be able to play or not. The idea would be if we could let it calm, we might be able to get him to Game 7."