Harrison's career-high scoring total included a 10-for-10 day at the free-throw line and helped carry the Wildcats (13-4, 3-1 SEC) to its fifth win in six games.
Julius Randle added 18 to the Kentucky attack and Aaron Harrison scored 14.
Jarnell Stokes led Tennessee (11-6, 2-2) with 20 points and 15 rebounds. The Volunteers lost for the second time in their last three games and fell to 4-35 all-time at Rupp Arena.
The Wildcats led 34-32 at halftime but fell behind early in the second half before getting back on track.
Darius Thompson scored a 3-point jumper with 3:02 to play to pull the Vols to within four points of the lead but they could get no closer.
Administration delays decision on Keystone XL once more
Putin thinks Obama would save him if he were drowning