Reinhart is the first player to score four goals in a Stanley Cup final since Montreal Canadiens’ Maurice Richard in 1957.
It took Reinhart four minutes and 36 seconds to open the scoring and the Panthers never looked back.
Matthew Tkachuk, who said after the game he had been playing with a torn adductor muscle and a hernia, doubled Florida’s lead by the end of the first quarter before Reinhart scored a further three unanswered.
Edmonton’s Vasily Podkolzin grabbed a consolation for the five-time Stanley Cup winners, but their last triumph in the competition came in 1989-90.
“We’re a dynasty,” Tkachuk said.
“I can’t believe this is what has happened… It just shows how unbelievable the group is, the depth.
“The culture down here is very, very unique. Hopefully, we can do it again.”