A first-quarter hook shot by James, 30, gave him 24,816 career points, passing longtime New York Knicks center Patrick Ewing.
"It's an honor," James said. "When I was growing up, you see these guys playing and you just hope that one day you can [too]. I always had dreams about being able to play in the NBA, and seeing what Pat and those guys were doing in the '90s with that New York Knick team facing the Pacers or facing the Bulls, or whoever they were going against, they were very tough-minded, and he was the cornerstone of the whole thing."
James finished with 23 points in the 114-88 Cavs win, giving him 24,837 for his career.
Ewing was just the latest legend to get bumped down by James' scoring march this season, as the four-time MVP already surpassed Charles Barkley, Allen Iverson and former teammate Ray Allen during the 2014-15 campaign.
"To pass him tonight in scoring, obviously, I never thought I'd even be a scorer as I am or even be able to put my name with those guys growing up," James said. "But I've been fortunate enough to be healthy, play with some great teammates that allow me to do what I need to do and I just try to give it back to the game as much as possible."
James currently is sixth in career scoring among active players. Jerry West is next up for James with 25,192 career points.
James, who went into Thursday's game averaging an Eastern Conference-best 25.7 points per game, is in his 12th season as a pro.
James became the youngest to score 24,000 points on Jan. 16. He has now scored at least 10 points in 637 straight games.
Information from The Associated Press was used in this report.