The Hornets led by 18 points entering the final period, but they were overwhelmed by a comeback that again brought the Lakers back to the .500 mark for the season.
Bryant scored 18 of his 42 points in the fourth period, during which the Lakers outscored New Orleans 33-9. Meeks had 19 points overall while Dwight Howard produced 20 points, 15 rebounds and four blocked shots.
New Orleans owned as much as a 25-point lead in the first half. The Hornets were held scoreless for the game's final 6:47 and wound up falling to the Lakers for the 10th straight time.
Eric Gordon led New Orleans with 18 points.
Los Angeles moved within 1 1/2 games of Utah for the eighth and final playoff spot in the Western Conference.