He missed, leaving him one shy of his first 50-point playoff game, muttering to himself after.
''That's the first time I've been disappointed in myself in a win,'' James said.
Then he smiled, realizing his performance left nothing to complain about.
James carried the Heat nearly the entire way until Bosh hit the shot that put Miami ahead for good - a play where James resisted the temptation to force a shot, instead passing to Mario Chalmers, who swung it to a wide-open Bosh.
Ray Allen followed with four free throws and James finished it off with one more, putting the Heat in position to wrap it up at home Wednesday in Game 5.
James was 16 of 24 from the field and 14 of 19 from the free throw line in matching the 49 points he scored for Cleveland against Orlando in the 2009 Eastern Conference finals. He missed his second free throw with 1.1 seconds left.
''He was what was needed on the road and that's what makes him the best player in the game,'' Heat coach Erik Spoelstra said.
Spoelstra talked to James about coming out in the fourth quarter, but had about as much success as the Nets' defenders.
''He asked me and I didn't know if he was serious or not, and what I told him I cannot say again,'' James said. ''So I wanted to finish out the game. I felt like it was a must-win for us.''
Joe Johnson scored 18 points for the Nets, who were 15 of 25 from 3-point range in their Game 3 victory but only 5 of 22 in this one. Paul Pierce added 16 points.
''This is very difficult to swallow,'' Nets center Kevin Garnett said. ''Hard to take, but it's what it is. Coulda, shoulda, woulda doesn't help us at this point.''
Dwyane Wade scored 15 points on the night his Heat postseason record of 46 points was shattered. Bosh finished with 12.
Miami pulled out a thrilling victory in a game neither team led by double digits and has won at least one road game in 14 straight series, breaking the record set by the Chicago Bulls from 1991-94.
Garnett's two free throws tied it with 2:30 remaining. Bosh then missed a pair of 3-pointers before getting a third crack at it in the corner in front of the Brooklyn bench for a 97-94 lead. Johnson then missed a jumper while trying to draw James' sixth foul - Johnson said afterward James ''flopped'' - and Allen's free throws put it away.
''Obviously the series is not over but we really have to have some urgency going to Miami and we've got to come out of there with one,'' Johnson said.
Wade scored 46 points against Boston in the 2010 playoffs, and James' best in a Heat uniform had also come against the Celtics, his memorable 45-point performance that saved Miami's season in Game 6 of the 2012 Eastern Conference finals.
Pierce, who asked to guard James after Game 1, was on the wrong end of this LeBron masterpiece.
James and the Heat had shrugged off a couple days of chatter from Pierce, who said the Nets weren't afraid of them. But things were testy at the start, with first-quarter technical fouls for James, Pierce, Shane Battier and Alan Anderson. Miami started quickly again and led 27-22 after one behind 12 points from James.
He opened the second on the bench and Brooklyn started with a 9-2 spurt to take its first lead at 31-29. James was a force once he returned - especially after a second foul against him seemed to get James more annoyed than any of Pierce's talking did.
James gave Pierce a glare after a thunderous slam later in the period, when he had 13 points in just 7 1/2 minutes, and the Heat led 56-49.
James had 13 straight Miami points in the third, but Brooklyn cut it to one on a few occasions before he made a pair of free throws to give Miami a 79-76 lead.
Notes: Mirza Teletovic was held to four points and missed all three 3-point attempts. He had been 11 of 19 in the series, Wade saying before the game it was ''red alert'' when he entered. ... As they have during postseason home games, the Nets had a Brooklyn-based entertainer announce their starting lineups. On Monday it was Mike D of the Beastie Boys. Denzel Washington, Spike Lee and Floyd Mayweather Jr. were also in the crowd.