The eighth regular season NBA game to be held in London was a home match for the 76ers, who led 57-48 at half-time and had won their past four games.
But Eastern Conference leaders Boston rallied strongly to extend their own winning run into a seventh match.
"It was pretty awesome," Celtics point guard Kyrie Irving said.
"It's something I'll remember for the rest of my life - the opportunity to come here, play this beautiful game and create some heart on the floor."
Irving scored 20 points to help his side towards victory, with shooting guard Jaylen Brown top scoring for the Celtics with 21.
Philadelphia shooting guard JJ Reddick was the night's most prolific scorer with 22 points, but his side still slipped to a defeat that leaves them ninth in the 15-team Eastern Conference rankings.
Before tip-off, both the American and British national anthems were played, while Irving and Philadelphia centre Joel Embiid addressed the crowd to thank them for their support.
Several Premier League footballers were among the spectators, including Manchester City winger Raheem Sterling, Chelsea forward Eden Hazard and Arsenal defender Hector Bellerin.
Atletico Madrid forward Antoine Griezmann, ex-Manchester United boss Sir Alex Ferguson and five-time Olympic gold medallist Sir Bradley Wiggins were also in attendance.