Dwyane Wade added 23 points and 10 rebounds and Shane Battier scored 18 points on 6-for-8 shooting from 3-point range for Miami.
James made 5 of 10 3s, all the while hounding Spurs star Tony Parker on defense to make the Heat the first back-to-back champs since the Lakers in 2009-10.
Tim Duncan had 24 points and 12 rebound for the Spurs, who were trying to become the first road team to win a finals Game 7 since Washington in 1978. Kawhi Leonard added 19 points and 16 rebounds.
Mario Chalmers scored 14 for Miami.
San Antonio lost for the first time in five finals appearances.