James, 35, scored 29 points to move to 33,655 career points, 12 more than former Lakers star Bryant, BBC Sport reported.
Kareem Abdul Jabbar, the ex-Lakers and Milwaukee Bucks center, is the NBA's all-time top scorer on 38,387 points.
Former Utah Jazz forward Karl Malone, who also briefly played for the Lakers, is second on 36,928.
"I'm happy just to be in any conversation with Kobe Bryant," said James.
"One of the all-time greatest basketball players to ever play, one of the all-time greatest Lakers.
"The man's got two jerseys hanging up in Staples Center. It's just crazy."
James, in his 17th NBA season, received a standing ovation from the Philadelphia crowd after scoring the basket that saw him pass Bryant's total in the third quarter.
Bryant tweeted, "Continuing to move the game forward. Much respect my brother."
Tobias Harris and Ben Simmons scored 29 and 28 points respectively to lead the Sixers to victory.
Top 10 all-time NBA scorers
Kareem Abdul-Jabbar – 38,387pts
Karl Malone – 36,928
LeBron James – 33,655
Kobe Bryant – 33,643
Michael Jordan – 32,292
Dirk Nowitzki – 31,560
Wilt Chamberlain – 31,419
Shaquille O'Neal – 28,596
Moses Malone – 27,409
Elvin Hayes – 27,313