A sluggish start saw the 76ers booed by the crowd as the Heat took a 51-39 half-time lead.
But Joel Embiid’s 23 points and 20 from Nicolas Batum’s, as well as 15 rebounds and five assists, led the 76ers comeback and secured a tense 105-104 win.
“There was lots of booing, but we stuck together,” said Embiid.
“It just shows that when I don’t play my best, I don’t get to my spots the whole game until the fourth quarter, we still find a way to win.”
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Jimmy Butler led the Heat’s first-half dominance with 19 points, five assists, four rebounds and five steals but suffered a knee injury and was limping by the end of the game.
The win secures the seventh seed spot for the 76ers in the Eastern conference, and they will face the New York Knicks in the first round of the play-offs.
Meanwhile, the Heat will face the Chicago Bulls in the play-in eliminator on Friday to decide the eighth and final play-off spot.
The Bulls reached the eliminator by beating the Atlanta Hawks 131-116.
Coby White starred in a comfortable Bulls victory with a career-best 42 points and Nikola Vucevic had 24 points and 12 rebounds.
The Bulls raced to a 40-22 lead at the end of the first quarter, but the Hawks kept themselves in contention and trailed by just three points with five minutes remaining.
But a three-pointer from Vucevic helped kickstart the Bulls’ momentum and they pulled away for the win.
Dejounte Murray scored 30 points as the Hawks’ season ended, with Trae Young and Clint Capela adding 22 points apiece and Bogdan Bogdanovic 21.
