James, 33, in his 15th season broke his tie with Michael Jordan when he scored his 10th (and 11th) point with 5:59 left in the first quarter.
The streak reached 867 on Friday night when the Cleveland Cavaliers beat the New Orleans Pelicans, a contest in which James poured in 27 on 12-of-24 shooting. The scoring streak extends back to the 2007-08 season.
"Any time I'm in the same group as the greats of this game, that's very humbling knowing where I come from", James told ESPN's Adam Schefter after the game.
"So anytime I'm in the same conversation with Mike and other great guys, it lets me know I'm doing the right thing and, hopefully, I can try to continue that".
Jordan's streak lasted from March 1986 until December 2001.
James, widely regarded as the best player of his generation, is now No. 7 on the list of all-time points leaders in the National Basketball Association behind only Kareem Abdul-Jabbar, Karl Malone, Kobe Bryant, Michael Jordan, Wilt Chamberlain and Dirk Nowitzki.
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A team record also fell after hosts Minnesota's Karl-Anthony Towns, 22, erupted for a career-high 56 points - eclipsing Mo Williams' 52 - to propel the Timberwolves to a 126-114 win over the Atlanta Hawks. He finished with 41 points, 10 rebounds and 8 assists for the game. "I think it's an incredible feat for him".
James' numbers back up his claim, as he is now leading the league in minutes and among the top three in both points and assists despite a continually changing roster surrounding him.
James came into Wednesday's game ranked No. 7 on the all-time scoring list with 30,814 points, needing 1,479 points to pass Jordan at No. 4 (32,292).
"I think I fell in love with the game because of Mike, just because of what he was able to accomplish", James said past year after breaking Jordan's playoff scoring record.
One of the few coaches who worked with Jordan and James, Cavaliers assistant Larry Drew was asked to compare the two hardwood heroes.
"Everywhere we go he gets a standing ovation", Smith said. I mean, he's just been phenomenal every game.