CHICAGO — No last-second shot. No fourth-quarter rally.

No record for LeBron James and the Miami Heat, either.

The Heat’s bid for NBA history ended Wednesday night when their 27-game winning streak was snapped by the Chicago Bulls, 101-97, setting off a raucous celebration inside United Center.

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Miami finished six shy of the 33-game record held by the 1971-72 Los Angeles Lakers.

Later, James said there was no shame in falling short.

‘‘It’s one of the best that this league has ever seen,’’ James said, referring to the streak that began on Super Bowl Sunday, Feb. 3. ‘‘We recognized that and rightfully so.’’

James tried to spur yet another comeback in the final minutes, getting mad after a rough foul. But the reigning MVP could never get the defending champions even or, more importantly, ahead.

With only .2 seconds left, James took the final inbounds pass in his own end, dropped the ball to allow time to expire, turned, and walked toward the exit.

Luol Deng scored 28 points, Carlos Boozer added 21 points and 17 rebounds, and the Bulls brought the Heat’s stampede to a screeching halt.

Miami’s superstar did all he could to keep the run going, scoring 32 points and even collecting a flagrant foul during a physical final few minutes.

‘‘We haven’t had a chance to really have a moment to know what we just did,’’ James said. ‘‘We had a moment, just very fortunate, very humbling and blessed to be part of this team and be part of a streak like that.’’

The Heat hadn’t lost since the Pacers beat them in Indianapolis Feb. 1. But after grinding out some close wins lately, including a rally from 27 down in Cleveland, no one counted them out until the final buzzer.

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. Not Wednesday.

‘‘We understand, probably more so later on in our careers, the significance of that. And then that was it,’’ Heat coach Erik Spoelstra said. ‘‘We took that moment to acknowledge it, to acknowledge each other, that experience, but it was never about the streak. We have a bigger goal, but also right now, it’s about ‘Are we getting better?' ’’

They walked off the floor stoically, not exchanging any handshakes or pleasantries with the Bulls.

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