Goals from Carter Verhaeghe and Sam Reinhart sealed a 4-3 series victory for the Panthers against an Oilers outfit who had rallied from 3-0 down to force a decisive game seven.
"I've been chasing that for a long time," Florida coach Paul Maurice said afterwards.
"It was perfect Florida Panther fashion - nothing's easy. Nothing's easy for us."
Edmonton had been bidding to become the first team from Canada since the Montreal Canadiens in 1993 to win the National Hockey League's championship.
The Oilers were also attempting to become only the second team in NHL history to overturn a 3-0 deficit to win the Stanley Cup.
But the Panthers - beaten by Vegas in last year's Stanley Cup Final - were in no mood to let victory slip away for a second straight year.
Roared on by their home fans at the Amerant Bank Arena in Sunrise, the Panthers surged into the lead after only 4min 27sec of the opening period.
Right-wing Evan Rodrigues smashed a shot from wide on the left and Verhaeghe was on hand in the goalmouth to tip in past Oilers goaltender Stuart Skinner.
Edmonton however silenced the home fans soon afterwards with a superb equaliser.
Cody Ceci's long pass split the Florida defence and was collected by Mattias Janmark, who glided towards the Panthers net and coolly tucked away a finish past Florida's Russian goaltender Sergei Bobrovsky.
Florida regained the lead however in the second period after a breathless passage of play that started with defender Dmitry Kulikov desperately shovelling away the puck on the goal line to prevent a certain Oilers score.
Florida's Sam Reinhart gathered and swept up the wing and let rip with a long-range snap shot that flew past Skinner for the score.
Sam Bennett almost made it 3-1 to Florida in the third period only to be denied by a brilliant Skinner save.
As the tension mounted, Edmonton laid siege to the Florida goal and only some last-ditch defending kept the Oilers at bay.
Relieved Panthers star Rodrigues meanwhile said Florida had been relaxed going into Monday's decider.
"They say this is the hardest trophy to win in sports, and you can't imagine how hard it is, until you do it," Rodrigues said.
"But getting to game seven, it took pressure off of us, and we did it the hard way. But it was a perfect outcome."