Miami's LeBron James, the sport's biggest star playing at the peak of his powers, had a game-high 37 points and pulled in 12 rebounds in a dominant performance while Dwyane Wade had 23 points.
"To be able to come on to our floor and do it, it's the ultimate," James, who delivered the perfect answer to those who doubted his killer instinct in the big games, said during an on-court interview.
"I can't worry about what everybody says about me. I am LeBron James from Akron, Ohio, from the inner city, I'm not even supposed to be here. I'm blessed."
James, named most valuable player of the Finals, shot 12-of-23 from the floor, including 5-of-10 three-pointers to lead Miami to their third NBA title and his second just two nights after the Heat's championship defence almost ended abruptly.
San Antonio, chasing a fifth NBA title, were just seconds away from clinching the championship on Tuesday before Miami staged an extraordinary comeback to win in overtime and force a decisive seventh game.
James, a four-times league MVP, sealed the victory with a jump shot with 27.9 seconds left, pumping his fist as the home crowd hailed their hero.
NBA Commissioner David Stern described the series as a "championship for the ages" which had "captivated a global audience" and there were generous words from the Heat for a Spurs team who pushed Miami all the way.
"It's no fun to lose, but we lost to a better team," said Spurs head coach Gregg Popovich. "And you can live with that as long as you've given your best. And I think we have."
The visitors made a great start, opening up a seven-point cushion in the first quarter and by three points late in the third quarter but came up just short.
Tim Duncan had 24 points and 12 rebounds for the Spurs while Kawhi Leonard had 19 points in the winner-take-all clash that had whipped basketball fans into a frenzy of excitement during a wildly fluctuating series full of escalating drama.
Courtside tickets for Thursday's game were selling on the secondary market for up to $30,000 and the game lived up to the hype with both teams fiercely contesting every possession.
Miami made yet another slow start and trailed by seven points less than five minutes into the game, a sloppy pass from James allowing Duncan an easy dunk.
A trademark turnaround jumper from Wade indicated the veteran from the Heat's 2006 title-winning team was in an aggressive mood and the introduction of Chris Andersen into the game injected some more energy into the Heat.
A pair of three pointers from Shane Battier brought roars from the crowd as Miami built an 18-16 lead by the end of the opening quarter.
James sat for the opening three minutes of the second quarter and the Spurs kept close. With just under seven minutes left in the half, the teams were tied at 27-27.
The brief rest paid off as James quickly gave Miami a six-point lead - he was fouled while scoring, putting away the free throw and then followed up with a three-pointer from deep.
But while the Heat were moving the ball well, typically, San Antonio kept close, helped by a huge three pointer from Gary Neal before a Duncan lay-up levelled the game at 40-40 with 1:55 left in the half.
Wade ended a fine first half performance with a fall-away jump shot to give the Heat a 46-44 lead at the break after scoring 14 points on 7-12 shooting and grabbing six rebounds.
James drained his third three-pointer early in the third quarter but two jumpers from the an impressive Kawhi Leonard, who had grabbed 10 first-half rebounds, ensured the Spurs kept with the pace.
Danny Green, who had been struggling with his shooting, sank a three-pointer to put San Antonio briefly a point ahead with 5:27 left in the third but James responded with two long rangers of his own, his five three-pointers a personal best in an NBA Finals game.
The Spurs led by two but Mario Chalmers beat the buzzer at the end of the third with a 30-footer to take Miami into the final quarter of the season with a 72-71 lead.
A Battier three gave the Heat an early four-point cushion and a Wade basket extended the lead to six with 7:14 remaining.
But San Antonio again responded and when Leonard drained a three-pointer it was a two-point game with two minutes left.
Chalmers missed two free throws but with 27 seconds left James delivered the killer blow with a vital jump shot and then made sure of victory when he snatched a Manu Ginobili pass, was fouled and put away both his free throws.
Wade added another from the free throw line before the home crowd erupted in celebration.