When Paul Pierce fouled out with 4:16 remaining, the 76ers had an opening to repeat their Game 7 magic from 30 years ago in Boston, but Rajon Rondo wouldn't let the Celtics falter in the deciding game of the Eastern Conference semifinals.
Rondo scored 11 of his 18 points in the final quarter, including nine in a row for his team right after Pierce left the game, and Boston beat Philadelphia, 85-75, Saturday night.
Rondo, who also had 10 rebounds and 10 assists, recorded his ninth career playoff triple-double.
"Rondo wants to run the team," Celtics coach Doc Rivers said. "He's a great quarterback. But tonight, obviously with Paul fouling out, he had to take charge of the team."
In the final seconds, fans at TD Garden turned their attention to Boston's next opponent with chants of "Beat the Heat!" Waiting for the Celtics in the conference finals will be LeBron James, Dwyane Wade and the rest of the Heat. That series starts Monday night in Miami.
This will be the third straight season that the Heat and Celtics will meet in the playoffs. Boston won in five games in 2010 in the first round and the Heat won in five last year in the semifinals.
Kevin Garnett had 18 points and 13 rebounds, while Brandon Bass scored 16 and Pierce ended with 15 points and nine rebounds.
Andre Iguodala had 18 points, while Jrue Holiday and Elton Brand both scored 15 for the Sixers, who played their first Game 7 since a win over Milwaukee at home in the 2001 Eastern Conference finals. Philadelphia dropped to 1-8 on the road in Game 7s, with that lone win coming at Boston in the 1982 Eastern Conference finals.
"I think we learned a lot," Holiday said. "We have a really young team. With a shortened season, we kind of learned on the fly. Playing against a veteran team like this really helped us grow."
Iguodala hit a left corner three-pointer with 4 1/2 minutes left, bringing the Sixers within 71-68. Pierce then plowed into Thaddeus Young and was gone from the game, but Rondo took over offensively.
The Sixers finished 35 percent from the field, mostly due to guards Lou Williams and Holiday, who combined to go 7-for-26.
The Sixers, though, who have just two players over 28 years old, pressured the Celtics defensively.
After missing their first 14 three-point shots, Ray Allen gave Boston some much-needed breathing room, nailing one from the top of the arc to ignite the home crowd and boost the margin to 60-54 early in the fourth quarter.
"It's not just about me, it's a team effort," Rondo said. "Ray made some big shots."
Each time the Sixers got within one possession, the Celtics had an answer, and Rondo took matters into his own hands.
"We were kind of down to Rondo and Kevin and pick-and-roll down the stretch," Rivers said. "We had been running it right before Paul went out. At least we had a rhythm in it and allowed us to keep running it."
After Garnett came up with a steal, Rondo found an opening on the left side and drove in for a layup and a 73-68 lead. Evan Turner missed a jumper and Rondo drained a shot from the top of the arc with his right foot cradling the three-point line.
"It served as momentum for Rondo," Brand said. "We didn't attack those guys as aggressively as we should have with such a prolific scorer on the bench. When he's out we try to trap Rondo, trap Garnett. But we just couldn't get to them."
Rondo's three-pointer from the right wing made it a 78-68 game with 2:09 left.
The eighth-seeded Sixers, who got past the Bulls in the first round after 2011 MVP Derrick Rose suffered a knee injury in Game 1, never got closer than seven the remainder of the contest.
"It was just our inability to score and it sort of plagued us throughout the season," Sixers coach Doug Collins said.
The Celtics missed just four of their 13 field goal attempts and went 9-of-10 from the charity stripe in the last quarter.
Boston raced out to a 10-2 lead, but the Sixers clawed back and tied it at 17 on an Iguodala three-ball. It was even at 20 going into the second.
The hosts didn't trail in the second, and when Bass stole an inbounds pass and raced in for a dunk, that provided the final points of the quarter, widening the gap to 41-33 at intermission.
Bass' foul line jumper gave Boston its first double-digit lead at 49-38, nearly four minutes into the third, but Philadelphia's quick hands paid dividends later in the quarter.
Holiday came up with a pair of steals, one leading to his own layup, and another a leak-out pass to Iguodala to get Collins' squad within 53-52 with 34.5 seconds left.
Garnett drained a left wing jumper over Lavoy Allen at the buzzer for a three- point margin going to the fourth.
Ray Allen had 11 points...Young had 10 rebounds...The second-seeded Heat, who finished off Indiana in six games Thursday, could be without Chris Bosh for the upcoming series. He's been sidelined with a strained abdominal muscle...The Celtics, seeded fourth, won three of the four meetings vs. Miami during the regular season...Boston is 18-4 at home in Game 7s.