The Vols looked like they were in for a cakewalk when Kentucky missed six of it first seven shots in the first half.
UK righted itself and came within 34-27 at the break and led 44-43 when Perry Stevenson sank two free throws with 12:24 left in the contest.
Tennessee was led by Tyler Smith's 15 points. Chris Lofton scored 14 and JaJuan Smith and Wayne Chism each added nine points for the Volunteers (26-3, 12-2), who bounced back from a 72-69 loss to Vanderbilt to win their 31st straight home game.
Kentucky got a game-high 17 points from Ramel Bradley. Stevenson scored 13 and Derrick Jasper scored nine points with eight assists for the injury-depleted Wildcats (16-11, 10-4), whose four-game winning streak ended in their first contest without star freshman forward Patrick Patterson (foot injury).
Celebrity Families of 2014 [PHOTOS]