Lakers veteran guard Derek Fisher forced the extra session when he nailed a game-tying 3-pointer with 14 seconds remaining after a furious fourth quarter comeback by the visitors.
Rasual Butler led the way with 31 points for New Orleans, which outscored Los Angeles 32-19 in the final period before the game was taken to OT by Fisher's three.
Bryant, the NBA's reigning MVP, shook off 10-for-27 regulation shooting by making all three of his shots in overtime as the NBA-best Lakers (45-10) won their third straight game.
"I wanted to attack, I was missing a lot of easy ones," Bryant told reporters. "It was important for me to take my time and gather myself for shots.
"We did OK tonight, but we still have a lot of room for improvement."
Spaniard Pau Gasol scored 20 points and 12 rebounds while Lamar Odom finished with 12 points and 17 rebounds for Los Angeles.
Hornets All-Star point guard Chris Paul had 21 points and added 16 assists before fouling out with 1:31 left in overtime.
Paul sparked a New Orleans fightback after Los Angeles had led 79-64 late in the third quarter.
The Hornets began the fourth with a 16-6 run and were up 98-95 when forward James Posey made a 3-pointer with just over a minute remaining in the game.
Posey later missed a potential game-tying 3-pointer with 12 seconds left in overtime.
The inconsistent Hornets (32-21) have now lost seven of their last 11 games.
The team is still without the services of center Tyson Chandler (ankle), who rejoined the team on Thursday after a trade that would have sent the 7-footer to the Oklahoma City Thunder was rescinded due to a failed physical.
The Lakers have gone 8-1 since starting center Andrew Bynum went down with a knee injury that sidelined him for the last three months of last year's regular season and playoffs.
"I can't say that I'm surprised. Last year we played a big chunk of games without him so we're used to playing without him," Bryant said.
"With that being said we can't wait to get him back—we miss his defensive presence in the interior."
