The Heat finished six games short of the record held by the 1971-72 Los Angeles Lakers.
Luol Deng scored 28 points, Carlos Boozer added 21 points and 17 rebounds, and the Bulls brought the Heat's pursuit of the record to a screeching halt despite another big game from James.
Miami's superstar did all he could to keep the run going, scoring 32 points in a physical final few minutes that saw the MVP even collect a flagrant foul.
The Heat hadn't lost since the Pacers beat them in Indianapolis on Feb. 1. But after grinding out some close wins lately, including a rally from 27 down in Cleveland, they simply came up short down the stretch in this one.
For the better part of two months, they were the NBA's comeback kings. They erased seven double-digit deficits during the streak. They found themselves trailing in the fourth quarter 11 times, and won them all.
And when they walked off the floor in Chicago, they were not happy. Faces were stoic as the Heat trudged toward the locker room. James turned and glared at one fan who grabbed at his head. Meanwhile, the Bulls whooped and slapped hands with anyone they could reach, with some acknowledging that being the team that snapped the streak meant plenty.
It will go down as the second-longest winning streak in the history of American major pro sports, behind only the Lakers. And some of those who helped that 33-game run become reality were openly cheering for the Heat as Miami's streak rolled along, with Jerry West among those saying that he believed the reigning champions had a real shot at pulling the feat off.
The streak began on Super Bowl Sunday in Toronto, a day when Heat players were mildly annoyed about having to miss football's title game. When San Francisco and Baltimore were to be playing, the Heat were to be flying home for a game the following night.
So team officials team changed course, as a surprise.
Miami beat Toronto that afternoon, then stayed in the city several more hours to watch the Super Bowl together, an event highlighted by Shane Battier giving an unplanned speech about appreciating little moments as a team.
For whatever reason, the Heat were unbeatable for nearly the next two months.
And they won games in a number of different ways.
They blew out good teams like the Los Angeles Clippers, Oklahoma City Thunder and the Bulls, then inexplicably struggled with lottery-bound Cleveland, Detroit, Sacramento, Charlotte and Orlando. They rallied from 13 points down in the final 8 minutes to beat Boston, from a 27-point third-quarter hole at Cleveland, and from 11-point deficits against Detroit and Charlotte - all those coming in a seven-day span, no less.
"There are several teams that can do it," Pistons guard Jose Calderon said, when asked what it would take for someone to beat Miami. "It's difficult to maintain this concentration every day. It will likely take everyone to have a bad day."
Even when those bad days happened, the Heat found ways to win.
A buzzer-beater by James against Orlando. Double-overtime against Sacramento. Huge comebacks. Whatever it took.
"To do something like this, everyone needs to step up," said Battier, who was part of a 32-game winning streak at Duke, a 22-gamer with the Houston Rockets and now played a role in this epic Heat run.
There were times when even the Heat themselves didn't know how long the streak was. Because it was interrupted by the All-Star break, Heat coach Erik Spoelstra was surprised when a staff member said something about Miami having won nine in a row. When it was at 24 games, Dwyane Wade made a reference to "23, 24, whatever it is."
They insisted they did not care about it, whatever the number was.
Heat President Pat Riley played for the Lakers team that won 33 in a row, and remained silent throughout Miami's streak, mainly because he rarely gives interviews these days but more so because the official team stance was that it simply did not matter. This season is championship-or-bust for Miami, one where nothing else other than raising yet another Larry O'Brien Trophy will satisfy.
"I understand the history of the game," James said after the streak reached 25. "I appreciate the history of the game. But this team has a bigger goal than winning a number of consecutive games in a row."
Still, the streak will go down as the story of the regular season.
When it started, Miami was 5½ games behind San Antonio for the overall NBA lead, only a half-game ahead of New York in the Eastern Conference race, held just a four-game edge over Atlanta in the Southeast Division and were the league's ninth-best road team in terms of winning percentage.
Funny what two months or so without losing can do.
The Heat now sit atop the overall NBA standings, gained 12 games over New York in the East entering Wednesday, put away the Hawks for good several weeks ago and are now, by far, the league's best road team. And with the streak over, all that's left now is getting ready for the postseason.