The Heat went 10 points up in the first quarter and stayed in front throughout, winning 129-101 with Jimmy Butler and Tyler Herro each scoring 24 points, BBC Sport reported.
They are one win behind sixth-placed Brooklyn Nets in the Eastern Conference with two regular-season games left.
The top six go straight into the play-offs and avoid having to qualify through the play-in tournament.
The 76ers, who are third in the Eastern Conference, have already secured their play-off spot.
Elsewhere, Kevin Durant scored 29 points, 12 of them in the final quarter, as the Phoenix Suns sealed the fourth seed in the Western Conference by beating the Denver Nuggets 119-115.
It was the Suns’ seventh consecutive win meaning they will enter the post-season, which starts next week, as one of the form teams.
The Nuggets clinched the top seed in the West through other results on Wednesday and rested a number of key players.
The Utah Jazz will not play in the post-season after they were beaten 114-98 by the Oklahoma City Thunder.
The Jazz needed a win to stand any chance of qualifying for the play-in tournament but Shai Gilgeous-Alexander’s 22 points helped seal a crucial win for the Thunder.
Oklahoma hold the last play-in place in 10th but could still be pipped by the Dallas Mavericks, who have two games to play over the final weekend while the Thunder only have one.
The Cleveland Cavaliers, who have already qualified for the play-offs, eased to a 118-94 win against the already-eliminated Orlando Magic.
Danny Green scored 21 points off the bench in a much-changed Cavaliers side.
Keita Bates-Diop scored 25 points as the San Antonio Spurs came from behind to beat the Portland Trail Blazers 129-127 in a match between two teams unable to qualify for the post-season.
The Blazers led 119-110 with six minutes remaining but San Antonio scored 13 points without reply, eight of them by Bates-Diop, to set up their win.