Bryant finished with 33 points, bringing the Lakers back from a 15-point deficit in the third period. Los Angeles won its second straight marathon, having defeated Memphis in double overtime Tuesday.
The Lakers were trailing by three when Bryant was fouled attempting a 3-pointer with 19 seconds left. He converted all three free throws to forge a 93-93 tie.
Jarrett Jack led New Orleans with a season-best 30 points.
Los Angeles has won four in a row and the Hornets have dropped 10 of their last 13.