Randle connected on 6-of-7 shots for the Wildcats (20-6, 10-3 SEC), winners of five in six games.
Aaron Harrison put in 17 points and James Young supplied 16 with six rebounds and five assists.
The Rebels (16-10, 7-6) got 22 points from Jarvis Summers.
Anthony Perez added 21 in a reserve role.
Celebrity Breakups and divorces of 2014 [PHOTOS]