LeBron James & The Miami Heat -- Champagne Poppin' til 6 AM

LeBron James is gonna be one exhausted (and hungover) NBA champion today ... 'cause the guy partied his face off 'til 6 AM ... and TMZ has the pics.

James and the rest of the world champion Miami Heat hit up the LIV Miami nightclub at the Fontainebleau Hotel ... where LeBron was drinking out of a 15-liter bottle of Ace of Spades champagne ... which usually run around $75k.

Sources at the club tell us ... LeBron grabbed the mic ... and rapped along with the music all night long ... while a bunch of his teammates puffed away on cigars.

At one point, 'Bron rapped along with the song "Riot" by 2 Chainz while LMFAO rocked out on a nearby stage.

After the Heat defeated the OKC Thunder in Game 5 last night ... a relieved LeBron exclaimed, "It's about damn time."