Philadelphia suffered a late collapse but recovered to hold off the Cleveland 98-97 as Ben Simmons made a successful NBA return from injury.
The 76ers, with Simmons starting after missing two games due to a shoulder strain, appeared in control of the contest on their home court on Tuesday.
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They held a seven-point lead late in the third-quarter, but missed 10 consecutive three-point attempts, became mired in turnovers and the Cavaliers went on a 17-5 run.
"We didn't start the fourth period well, so we were in a fist fight," 76ers coach Brett Brown said.
The Cavs were up 97-92 with two minutes left in the game.
The 76ers clawed their way back and with 21.9 seconds left and on a play drawn up by Brown in a time-out, All-Star centre Joe Embiid caught a pass from Tobias Harris for a game-winning dunk.
Kevin Love launched a three-pointer in the final seconds for a Cavs win, but it bounced off the rim.
Simmons had suffered a grade one AC joint sprain in his right shoulder last week against Utah and was expected to sit out the game.
But the Australian 23-year-old showed no ill-effects.
He played 34 minutes and had 15 points - largely from dunks, athletic tips around the rim and a reverse alley-oop.
He did not attempt a three-pointer but added five rebounds and six assists.
The 76ers were woeful from distance, missing 30 of 38 three-point attempts.
Harris played despite a stomach virus and it showed, with the forward missing all 11 three-point attempts although he scored four of the 76ers' last six points and threw the decisive assist to Embiid for the game-winner.
Australian point guard Matthew Dellavedova came off the bench for the Cavs and contributed four points in 12 minutes of game time.
Love and Jordan Clarkson led the Cavs with 20-point hauls.
Baynes brilliance not enough for Suns
In other games, Aron Baynes continued his strong start to the season with Phoenix but it was not enough for the Suns to beat the Los Angeles Lakers.
The Lakers won 123-115 in Phoenix with Baynes scoring 20 points, including sinking four of six three-point attempts, along with six rebounds and three assists.
LA's All-Star duo Anthony Davis and LeBron James had 24 and 19 points respectively.
Adelaide's Joe Ingles had a rough shooting night with just three points and missed all four three-point attempts, but his Utah side still beat Brooklyn 119-114.
Elsewhere Miami defeated Thon Maker's Detroit 117-108.
Also Indiana crushed the Oklahoma City 111-85, Chicago pounded the hapless New York Knicks 120-102 and Atlanta upset Denver 125-121.