Pau Gasol added 15 points, seven rebounds and six assists for the Lakers, who saw their season-high two-game slide come to an end. Andrew Bynum ended with 13 points and Derek Fisher 11 in the win. Lamar Odom gave 12 points and six boards.
Rudy Gay had 23 points for Memphis, which has dropped three in a row on the heels of a four-game win streak. O.J. Mayo had 22 points and six assists in defeat. Hakim Warrick recorded 14 points and Darko Milicic 11 with eight boards.
Bryant's layup brought the visitors within 86-85 with 5:58 left in the game.
Mayo's jumper and Mike Conley's three-point play gave Memphis a 91-85 lead moments later.
Bryant notched a couple of free throws and Trevor Ariza stole the ball from Mayo and dished to Odom for a dunk to bring the Lakers within 93-92 with 2:47 showing on the clock.
The teams traded baskets before a Mayo three eventually tied the game at 96.
The Lakers then brought the ball down and worked it around before Bryant drained a three as the shot clock expired for a 99-96 LA lead with 34.8 ticks left to play.
After a timeout, the Grizzlies inbounded the ball to Gay on the right wing. He launched a three that caromed off the rim, Fisher grabbed the rebound and was fouled by Gay with 31 seconds left. He went 1-for-2 at the stripe for a 100-96 advantage.
Memphis' next possession saw Gay dribble upcourt but lose control of the ball as he approached the lane. Odom picked up the loose ball and heaved a long pass to Ariza, who drew a foul with 22.8 seconds left.
LA went up 102-96 after Ariza hit both at the line, which all but sealed the win.
The teams played to a 25-25 stalemate at the conclusion of the first quarter, but the Grizzlies scored the final seven points of the half to take a 57-49 lead into the break.
Bryant's jumper sparked a 7-0 LA run and his free throw closed it out with 8:55 left in the third to give the Lakers a 60-59 lead.
The teams traded baskets before Marc Gasol's layup gave the Grizzlies an 80-77 advantage heading into the final 12 minutes.