After a lethargic loss in Game 3, the Lakers showed their composure to bounce back and seal victory with a stellar second-half performance.
James led all scorers with 28 points, 12 rebounds and eight assists.
His teammate Anthony Davis added 22 points, nine rebounds, four assists and four blocks.
Jimmy Butler and Tyler Herro finished 22 and 21 points, respectively, to lead the Heat.
Despite not producing one of his more prolific performances, James rated it as one of his best ever.
"I felt that vibe. I felt that pressure," James said after the game. "I felt like, for me personally, this was one of the biggest games of my career."
Tuesday's win gives the Lakers a 3-1 lead in the best-of-seven series, and brings them to the brink of a historic 17th championship -- the Lakers can close out the series if they win Game 5 on Friday.
A tightly fought first-half finished 49-47 to the Lakers.
LA came alive after the interval, with James scoring 20 of his 28 points in the second half.
Miami fought hard to fightback and level it at 83-83 with six minutes to play, but the Lakers pulled away again and didn't give up the lead.
With 40 seconds to play, Davis threw up a three pointer, beating his chest as it took the Lakers to an unassailable lead of 100-91.
James later said it was a "big-time play. [A] big-time moment."