The upset-minded Volunteers (8-8, 1-1 SEC) trailed 62-60 with 27 seconds to play but Darius Miller, who only had four points in the game, hit two free throws and Kidd-Gilchrist added one in the closing seconds to keep the game out of reach.
Terrence Jones was the only other Kentucky (17-1, 3-0) player in double figures with 10 points, but the Wildcats made 21-of-29 free throws and out-rebounded Tennessee 33-29. Kentucky has won nine consecutive games.
Cameron Tatum led Tennessee with 16 points. Jeronne Maymon scored 15 points and added 10 rebounds to the effort, but the Volunteers lost for the third time in their last four tries.