Bryant scored 29 points to become the fifth NBA player player to surpass the milestone. At 34, he did so a little over a year younger than the previous record-holder, Wilt Chamberlain.
Seventeen of Bryant's points, crucially, came in a first half when the Lakers were outplayed by the Hornets and they went in at half-time trailing by a point.
But Dwight Howard added 18 points and eight rebounds as the Lakers overwhelmed their young opponents in the second half.
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, while Smith made the decisive intervention after intercepting a pass from Michael Kidd-Gilchrist when the Bobcats looked set to snatch the win themselves.
Al Horford shone with 25 points and 12 rebounds as the Atlanta Hawks edged out the Denver Nuggets 108-104.
Ty Lawson scored 32 points in a losing cause for the Nuggets.
Tony Parker and Gary Neal had 22 points apiece as the San Antonio Spurs beat the Milwaukee Bucks 110-99 for their 15th win of the season.
Kevin Garnett scored 18 points and grabbed 10 rebounds against his old team as the Boston Celtics beat the Minnesota Timberwolves 104-94.
Al Jefferson had a big day with 31 points and 15 boards in the Utah Jazz's 87-81 win over the Orlando Magic.
DeMarcus Cousins had 25 points and 13 rebounds to lead the Sacramento Kings to a 107-100 win over the Toronto Raptors, who got 34 points from Kyle Lowry.
Twenty-three points from Marco Belinelli and 22 from Luol Deng saw the Chicago Bulls ease to a 95-85 victory over the Cleveland Cavaliers.
Klay Thompson led the Golden State Warriors with 27 points as they saw off the Detroit Pistons 104-97, the Indian Pacers beat the Portland Trail Blazers 99-92 and the Los Angeles Clippers overcame the Dallas Mavericks 112-90.