James went 6-for-6 from the free throw line in the frame, during which the Heat outscored the Pacers 33-16 to grab control of the deciding seventh game of the Eastern Conference finals.
The Heat superstar went 15-of-16 from the line overall and grabbed eight rounds as the top-seeded defending NBA champions reached the championship round for the third straight year.
Dwyane Wade pumped in 21 points and grabbed nine boards while Bosh added nine points, eight rebounds, three blocks and two steals en route to the victory.
The Heat now go on to face Western Conference champion San Antonio in the finals, which begin Thursday in Miami.
Indiana committed 21 turnovers and went just 6-of-20 from 3-point range in the loss as Paul George was held to seven points before fouling out.
Roy Hibbert led the third-seeded Pacers with 18 points.