The Grizzlies had led by as many as 20 points, but the Kings surged in the second half, pulling to within three points on Travis Outlaw's 3-pointer with 7:18 left in the game.
Randolph finished with 22 points and 10 rebounds and Conley provided 19 points with nine assists for the Grizzlies, who reached the .500 mark for the first time this season (5-5).
Outlaw ended with 18 points off the bench but it wasn't enough for the Kings, who fell to 1-7.
Notable deaths of 2014 [PHOTOS]
Arizona Cardinals player formally charged