Bryant reached the mark by making one free throw late in the second quarter of Thursday night's showdown against the Cleveland Cavaliers.
At 31 years, 151 days, Bryant got to 25,000 in 35 fewer days than Wilt Chamberlain, who finished his career with 31,419 points.
He finished the game with 31 points.
Earlier, Bryant was voted into his 12th All-Star game.
Next on the list for Bryant is Lakers legend Jerry West (25,192) and former Pacers guard Reggie Miller (25,279).
Kareem Abdul-Jabbar is the NBA's career leader with 38,387 points.
Information from the Associated Press was used in this report