San Antonio, which outscored the Heat 55-29 over the decisive second and third quarters, was paced in scoring by finals most valuable player Kawhi Leonard who had 22 points, while Argentina's Manu Ginobili added 19.
James, the four-time NBA MVP who led the Heat to titles the past two seasons, scored 31 points but was largely ineffective after the first quarter when he had 17 points.
The Spurs hit just one of their first 12 shots and trailled by 16 points early in the first quarter but outscored the Heat 25-11 in the decisive second quarter and led 47-40 at the half.
San Antonio, who lost to the Heat in the finals a year ago, opened the second half on a 18-4 run to seize a 65-44 lead, igniting the crowd hungry for the Spurs' first title since 2007 and their fifth overall.
A three-point shot by Australian Patty Mills and a jumper by Duncan hiked the Spurs' lead to 75-53 late in the third quarter and the rout was on.
James hit five of seven shots in the first quarter but nailed only five of 14 the rest of the way. The Heat shot 40 percent from the floor, including just seven of 25 from three-point range.
Miami was the first team to play in four straight finals since the Boston Celtics in 1984-87, and was hoping to become the first three-time champion since the Los Angeles Lakers more than a decade ago.
The title was the fifth for the Spurs' Tim Duncan, a 38-year-old, 14-time All-Star who has not yet said if he will continue to play.
"I know it is coming to an end," he said after Sunday's triumph. "I don't know if I will have a chance to do this again... It's a real emotional time."
Mercurial Spurs coach Gregg Popovich, who has coached Duncan to each of his titles, joins Phil Jackson, Red Auerbach, John Kundla and Pat Riley as the only coaches with five NBA crowns.
In the 2013 finals against Miami, the Spurs squandered a five-point lead in the last 28 seconds of regulation of Game Six to lose 103-100 in overtime.
The Spurs were so close to the title, the court was being lined with tape for the post-game award ceremony. Given new life, Miami went on to win Game Seven and the championship.
"We remembered what happened last year," Duncan said. "How it felt in our locker room and we used it, built on it and got back in."
San Antonio came back this year with the same roster, except for the addition of Italian Marco Bellinelli.
Quality minutes in the finals from Frenchman Boris Diaw, Mills and Brazilian Tiago Splitter, and improved play in the finals from Ginobili, lifted the Spurs to the title.
James played well overall in the finals but Dwyane Wade and Chris Bosh were unable to score consistently and the point guard pair of Mario Chalmers and Norris Cole underperformed.
Bosh hit six of 14 shots for 13 points on Sunday, while Wade totaled 11 points on four of 12 shooting.
The Heat's Big Three - James, Wade and Bosh - are all eligible to become free agents in the offseason, and, despite winning the Eastern Conference in each of their four seasons together, it is uncertain if they will return.
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