Terrence Jones had 15 points for Kentucky (21-8, 9-6 SEC), which have won four of its last five games but needed every bit of padding from a 40-point first half to hold off the Commodores (21-8, 9-6) down the stretch.
Kentucky led 40-29 at halftime but Vanderbilt went on a 13-2 run in the second half that cut the advantage to 57-56 with 7:56 to play.
Knight hit four clutch free throws and Jones sank three in the final 1:36 to hold on to the lead while Vanderbilt scored 3 points in the final 9 seconds.
Festus Ezeli led Vanderbilt with 22 points and 13 rebounds. John Jenkins chipped in with 16.