The hot-shooting Liggins scored 11 of his points in the first half and was 5-of-6 from the field and 7-of-8 from the free-throw line in the win, which ended a two-game conference losing streak for Kentucky (17-6, 5-4 SEC).
Harrellson also had six rebounds in the game. Terrence Jones had 11 boards to go with his 10 points.
Melvin Goins scored 16 points to lead Tennessee (15-9, 5-4) and Josh Bone added 13.
Kentucky led 35-28 at the half and embarked on a 13-0 run early in the second half to put the Wildcats in the driver's seat with a 48-30 advantage at the 16-minute mark. Kentucky maintained a double-digit lead the rest of the way.