PHILADELPHIA — The 76ers needed all the improbable tricks they could summon to even have a chance at winning their first play-in game in the team’s history.

Nicolas Batum hit game-shifting 3-pointers. Buddy Hield was in the mix. Even the promise of free chicken nuggets was enough to revive the offense and smother the boos from Philly fans inside the arena.

But, in crunch time, the game came down to Joel Embiid. It’s always Joel Embiid.

With the NBA MVP on the court, the Sixers proved they have a shot at a long postseason run — as long as he’s in the lineup.

Embiid had 23 points, 15 rebounds and one huge assist to Kelly Oubre Jr on a go-ahead three-point play that led the Sixers to a 105-104 win over the Miami Heat in the Eastern Conference play-in tournament on Wednesday night.

Embiid exploded out of a quiet game late in the fourth and carried the Sixers back from 14 down in the second half. Embiid, who missed 43 games this season and finished it on a surgically repaired left knee, was a non-factor as Batum and Hield sparked the 76ers in the second half. Batum had 20 points

“Lots of booing,” Embiid said, smiling. “We stuck together. It just shows you that I don’t play my best, I don’t get to my spots the whole game until the fourth quarter, and we still find a way to win.”

The Sixers earned the No 7 seed and advanced to play the second-seeded New York Knicks in the opening round of the Eastern Conference playoffs. Game 1 is Saturday at Madison Square Garden.

The Heat — who went from the play-in tourney to the NBA Finals a year ago — hosts Chicago on Friday night, with the winner getting the No 8 seed.

Embiid exploded out of a quiet game late in the fourth and carried the Sixers back from 14 down in the second half. Embiid, who missed 43 games this season and finished it on a surgically repaired left knee, was a non-factor as Batum and Hield sparked the 76ers in the second half. Batum had 20 points

“We won the game because of them,” Embiid said. “Those guys stepped up and we won the game.”

But, when the Sixers needed big buckets, who else was there but their big man?

Embiid buried a go-ahead 3-pointer from the top of the arc with 2:33 left in the game for a 93-91 lead that sent a crowd — that had just about booed the Sixers out of the building at the half — into a frenzy. After the Sixers blew that lead, Embiid again was clutch with a three-point play for a 96-94 lead.

With the game tied 96-all, Miami’s Tyler Herro was whistled for a backcourt violation. Embiid slipped the ball to Oubre under the hoop for the basket, the free throw and a 99-96 lead they would not give up.

The 76ers played this one like it was Game 7 — and with good reason. They like their chances against the upstart Knicks rather than playing for the No 8 seed and a date with the NBA’s best, the Boston Celtics.

That’s what Miami faces if it can get out of Friday’s game and make the playoffs under this format for the second straight season.

Herro — who hit a 3 in the final second before the 76ers lost the ball out of bounds as time expired — finished with 25 points. Jimmy Butler, perhaps slowed by a first-half knee injury, had 19.

“We will do this the hard way,” coach Erik Spoelstra said. “That has to be the path right now. We’re going to rest up, treat up, rally around each other and get ready for Friday. Again, embrace these competitive games. It will be competitive in front of our home fans.”

Butler had four steals in the first half, and gutted out two free throws after he slipped and appeared to tweak his right knee, perhaps a reason he scored only two points in the fourth. Butler said he would need an MRI on Thursday.

“It felt like I couldn’t do too much, which sucks with the timing of the game and everything,” Butler said. “I hope that I’m fine. I hope that I wake up tomorrow and can still stick-and-move. Right now, I can’t stay that’s the case.”

The Sixers rallied in the third, fueled perhaps by a free fast-food chicken promotion triggered when the Heat missed consecutive free throws with a nine-point lead.

With the crowd roaring for the first time all night, the Sixers took off — but not behind the usual suspects. Batum — acquired in the

James Harden deal with the Clippers — instead hit three 3s in the quarter that edged the Sixers within one possession of a tie game three times. Each time, the Sixers were stymied, none worse than when Embiid was stripped on a drive that could have knotted the game at 68-all. Kevin Love instead buried a 3 and the Heat took a 74-69 lead into the fourth.

After a few quick buckets put them up early, the Sixers caved and seemed downright befuddled by Miami’s zone. The Sixers were passive, and could not find a way to dump the ball inside to Embiid — the 7-footer waving his arm in vain for a ball that never came. And where was his help? All-Star guard Tyrese Maxey — who had three 50-point games this season — vanished and scored only nine points in the half. He finished with 19.

The boos from the Philly faithful reached their crescendo when the oft-maligned Tobias Harris ripped a page out of the book of Charles Smith, the 1990s Knicks star, when he missed no less than four “gimmes” at the bucket on one possession.

Harris was benched in the final minutes of the game.

They’ll need Harris playing close to an All-Star level moving forward, but for a game, Batum and Hield — and a heaped dose of Embiid — were enough for the Sixers.

“It’s just like we planned it,” a smiling team president Daryl Morey said in the locker room.