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.
Goran Dragic returned from four games missed with a foot injury, but it wasn't enough for Miami to force a Game 7 after falling behind 3-1 in the series.
The Lakers never trailed, first-year coach Frank Vogel shaking things up from the tip by starting Alex Caruso over Dwight Howard and shifting Davis to centre.
Caruso had only made two starts all season. The move paid off, as Los Angeles effectively put the game away by outscoring Miami 36-16 in the second quarter.
A 13-0 run in the period, capped by back-to-back 3-pointers from Caldwell-Pope, had the Lakers up by 30, 64-34, with 49.6 seconds left in the half.
The margin was 28 at the break, the second-largest halftime lead in NBA Finals history.
Davis and Caldwell-Pope each had 15 points at the break, and Rondo was a spark off the bench with 13 on 6-of-6 shooting.
Intermission did little to slow down Los Angeles, who led by as much as 36 before finishing the third quarter up 87-58.
Ahead 103-86 with 1:27 remaining, James and Davis went to the bench to begin celebrating with teammates.