Anthony Davis had 19 points and 15 rebounds, and Rajon Rondo scored 19 for the Lakers, who matched the Boston Celtics for most titles in league history with their first championship since 2010.
James, named the Finals' MVP, earned his fourth title with his third different team.
Bam Adebayo had 25 points and 10 rebounds, while Jimmy Butler and Jae Crowder scored 12 each for the Heat, whose Cinderella run at the NBA bubble came to an end.