Randle scored 17 points and nabbed 11 rebounds for his eighth double-double in 10 games for the Wildcats (8-2), who handed Boise State (8-1) its first loss of the season.
James Young led Kentucky with 21 points. Andrew and Aaron Harrison both scored 13 points.
Young scored 17 of his points in the first half, which ended with Kentucky ahead 41-31. Boise State did not have a foul-shot opportunity in the first half.
Anthony Drmic led Boise State with 18 points. And Derrick Marks added 14. Together, the Broncos' two leading scorers combined to shoot 13-for-40 from the field. Boise State shot 31.9 percent as a team compared to 52.9 percent for Kentucky.