Randle also had 11 rebounds in the Wildcats' (14-1, 4-1 SEC) sixth victory in their last seven starts.
Alex Caruso and Davonte Fitzgerald both scored 12 points for Texas A&M (12-6, 3-2). The Aggies have lost back-to-back games.
Kentucky led 34-27 at halftime and out-rebounded Texas A&M 42-24.
Kentucky shot 44 percent from the field compared to 37.3 percent for Texas A&M. The Wildcats fired off 21 shots from 3-point range and made six of them. The visitors opted to run their offense inside the arc and ended up 2-of-8 from 3-point territory.