Bryant also contributed 14 assists and nine boards as the Lakers held off a Sacramento rally down the stretch and stayed tied with the Utah Jazz for the eighth and final Western Conference playoff spot.
Bryant, playing with a bone spur in his foot, surpassed Wilt Chamberlain's total of 31,419 career points.
Dwight Howard provided 24 points and 15 rebounds for the Lakers.
The Kings got 21 points, nine rebounds and six assists from Tyreke Evans.
DeMarcus Cousins added 19 points and 11 boards for Sacramento.