The Wildcats broke open a one-point game with two big three-pointers by Koby Brea and some clutch free throws by Otega Oweh and Andrew Carr in the final 4:24.
Kentucky (17-7, 6-5 SEC) played the game without Jaxson Robinson and Kerr Kriisa, then lost Lamont Butler in the second half to a shoulder injury. Somehow, the Cats still found a way to grind out a crucial Quad 1 win.
Oweh and Ansley Almonor led Kentucky with 13 points each. Brea and Trent Noah both finished with 11 points. Travis Perry chipped in 8.
Zakai Zeigler led Tennessee (20-5, 7-5) with 17 points.