After the two-time defending champion Heat lost Game 3 in Brooklyn, James, the MVP runner-up, put Miami on his back in Game 4 Wednesday night, a 102-96 victory.
James scored 49 points, matching his career-high in the playoffs, and the Heat bounced back two days after having their eight-game postseason winning streak snapped.
James was 16-of-24 from the field and 14-of-19 at the foul line. He missed a free throw with 1.1 seconds left and a chance to reach 50. He also scored 49 points for Cleveland in Game 1 of the 2009 conference finals against Orlando.
"Whatever I needed to do to help us win, it needed to be done -- offensively, defensively, being the leader that I am on the floor, helping us overcome any adversity," said James.
Dwyane Wade added 15 points for the second-seeded Heat, Chris Bosh scored 12 and Ray Allen had 11 off the bench. Miami shot just shy of 53 percent.
Joe Johnson had 18 points to lead a well-rounded Nets effort. Paul Pierce chipped in 16 and Deron Williams and Shaun Livingston both scored 13.
James picked up his fifth foul and Kevin Garnett made two free throws to tie the score with less than a minute to go. Surrounded by Garnett and Pierce down low, James kicked the ball back to Mario Chalmers up top and Chalmers swung it to Bosh in the right corner.
Bosh buried the 3-pointer to break the tie, sparking an 8-2 Miami run to end the game.
James had that free throw with a hair over one second left for the magical 50- point plateau, but missed, and he muttered something to himself.
"That's the first time I've been disappointed in myself in a win," said James. "It definitely won't take away from the fact it was a huge game for us, being able to win this ball game.
"But it was a free throw. I hate missing free throws."
Now the series shifts back to South Beach, where the Heat are 4-0 this postseason. Brooklyn took both regular-season meetings in Miami and this veteran-laden squad isn't booking tee times just yet.
"The series is far from over," said Pierce. "We've got to go down there, try to get one game and force the series back at home. Just one, we've just got to get one game. That's the mindset."
Miami will try to advance to the Eastern Conference Finals for the fourth straight season.
If necessary, Game 6 would be Friday night in Brooklyn.