Boston were 99-98 behind following two Neemias Queta free throws before Maxey scored eight unanswered points to give his side a 107-98 lead with 15 seconds left.
“We started off well and then in the second quarter we kind of relaxed a little,” said Embiid. “Same thing with the start of the fourth.
“But we stuck together, closed it out.”
He added: “It means a lot. You can’t win alone, you need a team to be able win and everybody doing their job.”
Embiid had returned for the last four games of the series after an emergency appendectomy had ruled him out since 6 April.
“What changed in the series is Joel Embiid came back, and they’re a completely different team,” said Celtics coach Joe Mazzulla.
Boston star Jayson Tatum missed the decider because of a left knee issue, with Jaylen Brown top scoring for them with 33 points.
“Loved the looks that we got, loved the process that we had, but hate the result,” said Mazzulla.
