The Tigers out rebounded the Wildcats 46-32 and scored 44 points in the paint in their best all-around effort of the season.
Tim Quarterman scored a team-high 21 points and added 10 rebounds, while Craig Victor II posted the first double-double of his career with 15 points and 12 boards. Ben Simmons made it three double-doubles for the Tigers, scoring 14 points to go with 10 rebounds.
Senior Keith Hornsby only had nine points, but most of them came when LSU (9-5, 2-0) raced to a quick 13-6 lead on his back door layup and when his back-to-back three-pointers put the Tigers up by double digits 33-22 late in the first half.
Tyler Ulis, who had a game-high 23 points, pulled Kentucky (11-3, 1-1) to within 10 points at the break 37-27 by hitting a three-pointer before the halftime buzzer.
The Wildcats closed the gap to four points at the 9:36 mark of the second half on an Alex Poythress layup, but Quarterman and Victor each scored three pointers to restore LSU's double digit lead at 64-54 less than a minute later.
LSU bids for a 3-0 start in SEC play Saturday when the Tigers travel to Gainesville to play the Florida Gators.