The Heat led 49-44 at the half, with Chris Bosh having his best performance of the postseason with 17 first-half points, but the home side ran away with the game in the third.
Miami burst out with a 7-0 streak to grab a 12-point lead and LeBron took charge with two spectacular three-pointers and a ferocious dunk among his 14 points in the third.
James, who finished with 32 points, 10 rebounds and five assists, now has 74 career play-off games with at least 25 points, five rebounds and five assists, passing Michael Jordan for the most in NBA history.
The win puts Miami one victory away from a fourth straight appearance in the NBA Finals and a shot at a third straight title.
Miami have struggled with slow starts throughout the postseason but they were determined from the outset, grabbing a swift 8-0 advantage with all the points coming from Bosh.
"Coach drew up a play for me and I pretty much made my mind up that I was going to shoot it," said Bosh.
"After that, it's a funny thing but when my team-mates see me being aggressive like that and the shots do go in, they look for me a little bit more and I try to make their job a little easier."
While Miami credited Bosh and James for a strong performance, Indiana's Paul George felt the Heat had benefitted from favourable refereeing. Miami were given 34 free throws, double Indiana's total.
"I thought we outplayed them. It's just demoralizing when a game is lopsided, I'm sorry to say but that was the case again. How rare is it that we shoot 50 per cent, turn the ball over 14 times, out-rebound a team and lose?
"They made 30 free throws and that put them over the edge. I feel like we are just as aggressive as they are attacking the basket and making plays at the rim. Maybe this was just home cooking," he said.
James was having none of it.
"We did only have five turnovers and 20 points off their turnovers. That has nothing to do with the free throw line," he said.
It was a particularly fired-up performance from James but he rejected the idea that 'trash talk' in Game Three and further pre-game comments from Indiana's Lance Stephenson had contributed to his aggressive mindset.
"I don't need any motivation. I am motivated enough to try and get back to the finals," he said.
But George believed his team-mate's comments, where he claimed LeBron had shown 'weakness' in their on-court exchanges, had clearly backfired.
"Lance is young and that is a learning lesson for him. Sometimes you have got to watch what you say, you are on the big stage. Everything we say is going to be bulletin board material," he said.
Game Five of the best-of-seven series is on Wednesday in Indiana.
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