With a 44-point haul, Bryant surpassed Jerry West to become the Lakers all-time leading scorer but Rudy Gay spoilt the milestone with a crucial three-pointer with 29 seconds left to help seal the win.
Gay recorded 25 points while newly named All-Star Zach Randolph contributed 22 and 17 rebounds to help Memphis (26-21) break a string of two straight losses and avenge a November 6 defeat to the Lakers.
"These young guys stepped up and played great," Randolph told reporters. "Rudy hit big shots. O.J. (Mayo) played good. It was just a good all-around game for the whole team."
After Gay's three put the Grizzlies up 95-90, Bryant made a triple of his own, and the defending champions had one final possession that saw Ron Artest miss a three-pointer as time expired.
Los Angeles pulled level thanks to an 18-6 run in the third and the fourth quarter went back and forth before Artest missed the final open shot.
For the Lakers, Bryant was aggressive all evening as he entered the game needing 29 points to surpass West, who was the Lakers general manager when Bryant was drafted.
The four-time NBA champion achieved the record on a dunk with 4:13 left in the third and completed the game with a career total of 25,208 points.
"It's a great honor. With all the great players who have played here and the rich tradition we have it's a great accomplishment," Bryant said.
"(West) taught me so much when I was 17 and showed me a lot about the game. Even though I'm passing him in the record books it feels like it's still both of us."
Los Angeles coach Phil Jackson missed the chance to make it a landmark double, the defeat meant he remains tied with Pat Riley as the all-time winningest coach for the Lakers on 533 victories.
(Writing by Jahmal Corner; Edited by Patrick Johnston)