Star guard Kyrie Irving scored 20 points with seven assists and six rebounds for the Celtics. Jaylen Brown scored 21 points and Marcus Morris had 19 with eight rebounds as the Eastern Conference-leading Celtics stretched their NBA winning streak to seven games.
Rookie Jayson Tatum helped turn the tide, scoring 11 of his 16 points in the decisive third period.
"I don't think we were ready for the punch they gave us in the first half," Celtics coach Brad Stevens acknowledged. "There was no real panic, but we had to play a lot better than we were."
The 76ers had come out strong, with JJ Redick scoring 13 of his 22 points in the first half.
Cameroon's Joel Embiid added 16 points and Aussie Ben Simmons chipped in 15 for Philadelphia and for a time it looked as if the eighth regular-season NBA game to be played in London could see the 76ers on the right side of the kind of blowout that fans there saw last year, when the Denver Nuggets trounced the Indiana Pacers 140-112.
But the Celtics tightened the screws defensively and closed out the second quarter on a 15-3 scoring run before out-scoring the Sixers 37-22 to seize control in the third period.
"We stayed the course," Stevens said. "We've done that all year."
Tatum, like Simmons a rookie of the year candidate, came alive in the third, making his first five shots as Boston cut the deficit to one point.
Boston took the lead for the first time on a dunk by Daniel Theis that made it 69-68 with six minutes left in the third.
Boston joined the NBA champion Golden State Warriors as the only teams to come back from 20-point deficits in more than one game this season.
Irving acknowledged that their offense wasn't flowing early as they played for the first time since edging the Brooklyn Nets on Saturday.
But he added that once they got the ball moving and began to push the pace, the Celtics never doubted they could come all the way back.
As the Celtics built their lead to as many as 19 points in the fourth quarter, Irving heard some chants of "M-V-P".
"That was pretty awesome over here in London, man, in the O2," said the Australian-born Irving, who opted out of a chance to play for Australia at the 2012 London Oympics in order to pursue an international career with the USA. "This is something I'll remember for the rest of my life."
The host of Premier League stars in attendance included Hector Bellerin among a contingent of Arsenal players and Chelsea's Eden Hazard.
Manchester City's Kevin De Bruyne was also on hand, as were Manchester United's iconic former manager Alex Ferguson and former Chelsea midfielder Michael Ballack and British cycling hero Bradley Wiggins.