After having to rally in each of its previous games, the Wildcats (4-1) led throughout against the Trojans (2-3). They built a double-digit lead early and extended it to 21 twice in the second half, a needed cushion as Troy fought back to within eight on Wesley Person's three-point play with 1:08 remaining.
Knox came up with the last of Kentucky's season-high 53 rebounds that preserved its second victory in the Adolph Rupp Classic named for the legendary coach.
Quade Green had 13 points and reserve forward Wenyen Gabriel 12 for the Wildcats. Hamidou Diallo had a career-high 10 rebounds to go along with eight points.
Person had 17 points and Jordon Varnado and Kevin Baker 15 each for Troy.