Bryant drove to the bucket to break a 97-97 with 1:25 to play and then hit a 19-foot jumper for the eventual game winner with 52 seconds left in regulation to give Los Angeles its third consecutive win.
The comeback dashed Charlotte's hopes of ending a 12-game losing skid.
Dwight Howard added 16 points and 18 rebounds to the Lakers offense. Pau Gasol scored 10 points and snagged nine rebounds. Gasol played 29 minutes in his first game since being sidelined with a knee injury.
Kemba Walker led the Bobcats with 28 points. Walker made a bid to win it with 5 seconds to play but his drive for a layup was blocked by Howard.
Charlotte led 84-79 at the start of the fourth quarter but did not score again until Walker hit a jumper with 8:33 to play.