Randolph scored on a layup with 16 seconds to put the Grizzlies in front by three and he added two free throws with 9 seconds remaining for a five-point cushion.
Memphis handed the Lakers their third home loss in six games with Randolph scoring 28 points to go with 11 rebounds.
Marc Gasol flirted with a triple-double, scoring 18 points, grabbing eight rebounds and handing out eight assists.
A relatively low total of 30 fouls were called in the game and the teams combined to take only 25 free throws. Memphis made all 14 it attempted.
Celebrity Families of 2014 [PHOTOS]