The last of Bryant's points came with 29 seconds to play and boosted the Lakers to a four-point lead, bringing them their fourth straight victory.
The Clippers had a six-game winning streak come to an end and fell 2 1/2 games behind the Lakers for the Pacific Division lead.
The Lakers held an 11-point lead heading into the fourth quarter but the Clippers went on an 8-0 run to open the period and eventually tied it with 4:14 to play on a jumper by Chris Paul.
Ramon Sessions then put the Lakers in front for good with a free throw, touching off a game-ending 11-6 surge.
Andrew Bynum led the Lakers with 36 points, making 13-of-20 from the field. The Lakers shot 51 percent.
Caron Butler had 28 points for the Clippers and Paul had 22. The Lakers won the season series 2-1.
18-year-old elf alleges mall Santa pinched her buttocks on the job
Caroline Berg Eriksen: Soccer player's wife triggers debate with post-birth selfie