The 76ers, winners of 10 games just two seasons ago, are in the second round of the Eastern Conference playoffs for the first time since 2012.
They await the winner of Milwaukee-Boston. The Celtics lead the series 3-2.
The Sixers won the series 4-1 and turned the Wells Fargo Center into the wildest house party in the city. Embiid had 19 points and 12 rebounds, Simmons had 14 points and 10 boards, and the entire team had rappers, politicians, actors and kids dancing along for the ride.
Mill made a dramatic return hours after Pennsylvania's highest court ordered him freed while he appeals decade-old gun and drug convictions.
He was taken from prison by helicopter to Philadelphia, where he rang the ceremonial bell at the start of Game 5.
"Welcome home Meek Mill," was about all that was heard from the public address announcer as wild cheers drowned out the rest. Mill sat courtside next to actor and noted Sixers fan Kevin Hart and Sixers co-owner Michael Rubin.
Hart grabbed the mic after the game and yelled, "Let's give it up for Joel Embiid!"
Before the game, Mill visited privately with the Sixers in their locker room.
Hart talked trash, wandered onto the edge of the court to rile up fans and palled around with Mill as the young and gettin' it Sixers proved they just might be the team to beat in the East.
They'll have plenty of time to rest and recover - Embiid again played in a black mask to guard a face injury - with the other Eastern Conference playoff series expected to stretch into the weekend.
The 76ers were buzzing once Mill's release made headline news in the city. Rubin had organized prison trips with Embiid, Simmons and Markelle Fultz, and the rapper's songs played in the locker room and during warmups.
Simmons called Mill's presence "amazing."
"Just having someone that looks out for us, all of us here, it would just mean a lot for him to be back in Philly, in the city of Philadelphia with the fans, especially with a game like that tonight," Simmons said.
Mill breezed into the locker room about 45 minutes before tip and hugged some of the Sixers. Mill was met with a crush of media and celebrity fans as he tried to take his courtside seat. Eagles owner Jeffrey Lurie and retired boxing great Bernard Hopkins sat near Hart and Mill, and Democratic Gov. Tom Wolf joined them in the second half. The national champion Villanova Wildcats posed for pictures with Mill in the locker room.
What they saw was just the latest beatdown from a franchise whose maligned rebuild has morphed into the one of the trendiest terms in sports.
The Sixers outscored the Heat by 14 in the third quarter to snap a tie game and had fans belting "Trust the Process!"
Goran Dragic was whistled for a technical after slapping Simmons on the backside of his head, and that got the crowd howling early in the third. Simmons kept his cool - the rookie is rarely rattled - and made the Heat pay. JJ Redick sank the free throw off the technical, and Simmons kicked the ball out to Robert Covington on the possession for a 3 and a 54-48 lead. Redick followed with his third 3, and Philly was litty again.
Redick, who scored 27, sank the dagger late in the fourth that sent confetti flying, team flags waving and put a late-night celebration on deck.
Heat: Josh Richardson played with a sprained left shoulder. He picked up three fouls in his first 2 minutes. ... James Johnson was hit with personal and technical fouls late in the fourth that ended a 10-0 Miami run. ... Dwyane Wade is considering retirement. ... Justise Winslow led the Heat with 18 points.
76ers: Redick was whistled for a technical foul in the first half. ... Missed 10 of 12 3s in the first half.
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