LeBron James got the first official statistic of his NBA career on a rebound. His next entry on the stat sheet was an assist.

Even then, points weren’t the priority. They never were.

Somehow, Mr. James became the most prolific scorer in NBA history anyway. It finally happened Tuesday night, the kid from Akron, Ohio, connecting on a step-back jumper to push his career total to 38,388 points and break the record that Kareem Abdul-Jabbar held for nearly 39 years.

Mr. James outstretched his arms after his 36th point of the night for the Los Angeles Lakers, threw both hands in the air, then smiled. Mr. Abdul-Jabbar rose from his seat and clapped. The game was stopped as members of Mr. James’s family, including his mother, his wife, and their three children, took the floor for a ceremony recognizing the moment.

“It’s never gotten my juices flowing,” Mr. James told the Associated Press, when asked what the scoring record means to him. “I’m there now because I never, ever thought about it. The only thing I ever thought about was winning championships, maybe a couple MVPs, maybe defensive player of the year. But scoring championships and records, I’m telling you, that was never on my mind.”

Mr. Abdul-Jabbar — a longtime Laker and one of many celebrities and sports stars who made sure they were there to see history — became the league’s all-time leading scorer on April 5, 1984, and wound up retiring in 1989 with 38,387 points. It was a record that some thought would last forever, with very few even coming close. Karl Malone retired 1,459 points behind Mr. Abdul-Jabbar, Kobe Bryant was 4,744 points shy, and Michael Jordan was 6,095 points away.

Mr. James passed them all, then caught Mr. Abdul-Jabbar, too. The 38-year-old — who finished with 38 points in the Lakers’ 133-130 loss — did it in his 20th season. Mr. Abdul-Jabbar also played 20 NBA seasons.

“You’ve got to give him credit for just the way that he planned to last and to dominate,” Mr. Abdul-Jabbar told TNT.

And now, King James — a moniker he’s had since high school, when he was just a kid from Akron — is the NBA’s scoring king, with 38,390 points and counting.

“A record that has stood for nearly 40 years, which many people thought would never be broken,” the NBA commissioner, Adam Silver, said.

Mr. Abdul-Jabbar held the ball aloft, then handed it to Mr. James, the ceremonial passing of the torch. They posed for photos with Mr. Silver, then with one another. Mr. James wiped away tears from his eyes, then addressed the crowd.

“I just want to say, thank you to the Laker faithful. You guys are one of a kind,” Mr. James said. “To be able to be in the presence of such a legend as great as Kareem, it’s very humbling. Please give a standing ovation to the Captain, please.”

Mr. James then thanked his family and those who have supported him, including Mr. Silver and a late NBA commissioner, David Stern. “I thank you guys so much for allowing me to be a part of something I’ve always dreamed about,” Mr. James said.

At least 16 different players have, technically, been the all-time leading scorer in league history — most of those coming in the opening month of the league’s existence in 1946, when everybody was starting from zero and nine different players were atop the scoring list in the first 16 days.

Only six have ended a season officially as the all-time leader: Joe Fulks, George Mikan, Dolph Schayes, Bob Pettit, Wilt Chamberlain, and Mr. Abdul-Jabbar.

Mr. James will be the seventh name on that list, and he’s likely to stay there for a long time. No active player is within 10,000 points. He is under contract for two more years and is on pace to become the league’s first 40,000-point scorer sometime next season.

“Nobody will ever, ever touch it,” a Cleveland forward, Kevin Love, a teammate of Mr. James on the 2016 title team, said. “The scoring record now will never be eclipsed. I don’t care. It will never, ever be touched. It will never happen again.”

Mr. James could have had the scoring record long ago, if so inclined. But he always preferred passing. Mr. James is behind only John Stockton, Jason Kidd, and Chris Paul on the all-time assists list. None of them were, or are, close to the scorer that Mr. James is. Of that group, Mr. Paul comes closest, ranking 38th in NBA history.

Mr. Paul is 17,000 points behind the new scoring king.

“I hadn’t thought of it that way, but that is very true,” Mr. Silver told the AP in advance of the record-setting night. “I think it even adds — right? — to this accomplishment for a guy who became a scorer because he determined that’s what was necessary to win. 

Mr. James is the only member of the NBA’s triple-quintuple club: at least 10,000 points, 10,000 rebounds, and 10,000 assists. There are 44 players to reach five digits in two of those categories.

Mr. James will almost certainly be the NBA’s all-time leader in earnings whenever he retires; when adding in the $97 million he’ll make over the next two seasons, he’ll be past $500 million in on-court salary alone. He’s a 19-time All-Star selection, tying a record of Mr. Abdul-Jabbar. If he plays in the game on February 19 in Salt Lake City, he’ll set a record for appearances.

Others, maybe, have been this good. That’s always a debate. But no one has ever been this good, for this long. Mr. James — a two-time champion in Miami, a champion in Cleveland in 2016, and a champion with the Lakers in 2020 — is averaging 30 points per game in his 20th season; only three other players have averaged more than 10 points per game this deep into their careers. 

“I never did the, ‘Okay, if I play this amount of time and I average this’ thing,” Mr. James said. “I’ve never done that with anything in my career. I always said, ‘If it happens, it happens.’”

It happened.