LeBron James clinched the winning basket with 10 seconds remaining after Boston failed to stop the Heat setting the NBA's second-longest win streak outright.
NBA: Miami Heat extend winning streak with narrow win over Celtics
Miami Heat staked a claim to be the best side of the modern NBA era after a late win against the Boston Celtics saw them confirm the second-longest winning streak in the competition's history.
The defending NBA champions made it 23 consecutive wins with a 105-103 win at Boston to edge them past the 2007-08 Houston Rockets side in the record books.
Only the 1971-72 Los Angeles Lakers, who own the all-time record of 33 wins in a row, have had a longer NBA win streak than Miami's epic run.
But it took a LeBron James basket with just 10.5 seconds remaining of the game for Miami after a battling performance by Boston.
"We were down a lot of times tonight, more than we would like to be," James said.
"But we kept our chemistry going and got one more play. It was a hostile environment. For us to come in here and get a win today was awesome."
James scored 37 points and added 12 assists and seven rebounds for the Heat while Mario Chalmers added 21 points, Dwyane Wade contributed 16 and Chris Bosh netted 13 for Miami.
Celtics had ended Houston's historic run in 2008, and came close to doing the same to Miami Miami despite the absence through injury of centre Kevin Garnett.
Jeff Green hit a career-high 43 points, the most for any Boston player this season, and the most surrendered by the Heat to any opposing player all season.
After an 18-4 Miami run gave the Heat the lead, Boston's Avery Bradley, who missed eight of his first 10 shots, sank a 3-pointer from the left corner to put the Celtics ahead 103-101 with 1:49 remaining.
James answered with a layup to equalise at 103-103 and each team made a stop defensively to leave the ball in Boston's hands. Brandon Bass missed a layup and Dwyane Wade rebounded for Miami as the tension mounted in the last seconds.
James took the ball and sank a 20-foot jumper while being guarded by Green to put Miami ahead by the final margin.
Miami now travel to Cleveland for tomorrow's match with the Lakers' record in their sights.
Elsewhere the Denver Nuggets also continued their winning run, narrowly clinching a 12th straight success thanks to a 119-118 overtime victory against the Chicago Bulls.
A late surge from Luis Scola, who scored all 14 of his points in the final quarter, led the Phoenix Suns to a comprehensive 99-76 win against the Los Angeles Lakers.
The New York Knicks ended a four-game losing streak by seeing off the Utah Jazz 90-83, JR Smith contributing 20 points and Raymond Felton 19 for the victors.
The Washington Wizards' three-game winning run ended in a 119-114 loss against the Bobcats in Charlotte. Jrue Holiday scored 27 points, including a couple of decisive late free throws, as the Philadelphia 76ers edged the Portland Trail Blazers 101-100, while the Detroit Pistons suffered their ninth consecutive defeat, going down 119-82 against the Brooklyn Nets.
Gerald Green's 20 points helped the Indiana Pacers topple the Cavaliers 111-90 in Cleveland, 24 points from Darren Collison lifted the Dallas Mavericks to a 127-113 triumph over the Atlanta Hawks, the Memphis Grizzlies overcame the Minnesota Timberwolves 92-77 and the Golden State Warriors cruised past the New Orleans Hornets 93-72.
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