San Antonio trailed by 16 in the game's first seven minutes but outscored the Heat 55-29 over the decisive second and third quarters and were never threatened.
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.
"That's how team basketball should be played," James said of the Spurs. "It's selfless. Guys move, cut, pass, you've got a shot, you take it, but it's all for the team and it's never about the individual. That's the brand of basketball.
"They were the much better team."
The Spurs were paced in scoring by the Finals' MVP Kawhi Leonard who had 22 points, while Argentina's Manu Ginobili added 19.
San Antonio hit just one of its first 12 shots and trailed 22-6 but outscored the Heat 25-11 in the 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 Patrick Mills and a jumper by Duncan hiked the Spurs' lead to 75-53 late in the third quarter and the rout was on.
"It just feels like a dream to me," said Leonard. "This is my second finals appearance in my third year. I've been just progressing each year and the team has also.
"Losing in the semifinals my first year, and losing the championship my second year, and now winning in my third year, it just makes you believe in your craft and your hard work."
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 successive finals since the Boston Celtics in 1984-87, and were 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.
"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.
"They're that good," Bosh said of the Spurs.
"I thought we'd get over the hump and we never did. They dominated us in this series, frankly speaking, and they deserve everything that they got."
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.