Randle missed only two of his 10 shots from the field and hit 13 free throws for the Wildcats (9-3), who scored 52 points in the second half to break the game open.
Aaron Harrison scored 23 for Kentucky and Willie Cauley-Stein finished with 16 points.
Craig Bradshaw led Belmont (8-5) with 22 points and Drew Windler scored 21. The Bruins lost their third consecutive game.
Belmont led 43-41 at halftime and shot a respectable 46.9 percent from the field for the entire game; however, they lost the rebounding battle 42-25 and committed 29 personal fouls, which sent Kentucky to the line 36 times.