Bryant scored 29 points to become the fifth NBA player to exceed the milestone. At 34, he reached the landmark a little over a year younger than the previous record-holder, Wilt Chamberlain.
Crucially, seventeen of Bryant's points came in the first half when the Lakers were outplayed by the Hornets, going in at half-time trailing by a point.
However, Dwight Howard added 18 points and eight rebounds as the Lakers stunned their young opponents in the second half.
Elsewhere, JR Smith scored a jump shot on the buzzer to give the New York Knicks a 100-98 win over the Charlotte Bobcats.
Carmelo Anthony scored 23 points for the Knicks, with Smith making the pivotal intervention after intercepting a pass from Michael Kidd-Gilchrist when the Bobcats looked set to snatch the win themselves.
It was Al Horford who shone with 25 points and 12 rebounds as the Atlanta Hawks edged out the Denver Nuggets 108-104.
Ty Lawson recorded 32 points in a losing cause for the Nuggets.