San Antonio, which outscored the Heat 55-29 over the decisive second and third quarters, was paced in scoring by Kawhi Leonard who had 22, while Manu Ginobili added 19.
James, 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 faced a 22-6 first-quarter deficit 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.