Randle's 17 first-half points staked Kentucky (10-3) to a 41-36 halftime lead before the 6-foot-9 forward went to the locker room early in the second with leg cramps. He returned but cramped again and spent the rest of the game on the bench.
The Harrison twins amply filled the void, turning a 52-51 deficit with 11:01 remaining into a 68-58 lead with four minutes left. Andrew Harrison and James each scored 18 points with Young adding a key 3-pointer during the 17-6 run that helped Kentucky beat its in-state archrival for the fifth time in six meetings.
Russ Smith scored 19 points but was just 5 of 10 from the foul line for Louisville (11-2).