A three-point play with 3:55 to go saw James surpass Wilt Chamberlain to take the number five spot.
Finishing with 44 points, as well as 10 rebounds and nine assists, his career total increased to 31,425 points during a fourth win in a row for the Lakers.
The Detroit Pistons overcame a 19-point deficit to claim a 106-104 victory over coach Dwane Casey’s former team the Toronto Raptors.
A 23-9 run at the start of the final quarter brought the Pistons back into contention, before Reggie Bullock’s shot on the buzzer clinched the win.
Blake Griffin led the way with 30 points and 12 rebounds.
The Milwaukee Bucks suffered their first home loss of the season thanks to a late surge from the Memphis Grizzlies.
Despite squandering a 15-point lead in the third quarter, Memphis used a 15-2 run in the fourth to post a 116-113 victory.
Mike Conley, who finished on 26 points, helped put the side four points ahead with nine seconds remaining.
Jimmy Butler made his debut for the Philadelphia 76ers, but could not help his side hold off a late comeback from the Orlando Magic.
The Magic went on a 21-0 run in the fourth quarter to wipe out a 16-point deficit, before Terrence Ross had a tie-breaking three-pointer in the final seconds to lift the side to a 111-106 win.
Butler’s former team the Minnesota Timberwolves had more joy, defeating the New Orleans Pelicans 107-100.
Karl-Anthony Towns recorded 25 points and 16 rebounds while Andrew Wiggins scored 23 points.
Meanwhile, Paul George finished with a season-high 35 points as the Oklahoma City Thunder trounced the New York Knicks 128-103, while the Boston Celtics recorded their biggest-margin win of the season, routing the Chicago Bulls 111-82.
The Cleveland Cavaliers continued to struggle, with a 119-95 loss to the Washington Wizards putting them on 2-12 for the season.
And the Miami Heat snapped a three-game skid as they beat the Brooklyn Nets 120-107.
Elsewhere, the Dallas Mavericks gave up just nine points in the fourth quarter to claim a convincing 118-68 win over the Utah Jazz, while the Phoenix Suns ended a four-game losing streak in their 116-96 defeat of the San Antonio Spurs.