Kevin Knox added 16 points for Kentucky (12-2, 2-0), which was playing on an opponent's home floor for the first time this season. The Wildcats visit No. 23 Tennessee on Saturday.
"P.J. played well. He's starting to lead the team," Kentucky coach John Calipari said. "We're getting that will to win."
It was the SEC opener for LSU (9-4, 0-1), which visits No. 11 Texas A&M on Saturday.
Duop Reath led the Tigers with 24 points, Tremont Waters scored 18 and Aaron Epps had 13.
LSU had a 38-31 lead early in the second half before Hamidou Diallo made a basket and a 3-pointer to start a 14-4 run that gave Kentucky a 45-42 lead.
The teams exchanged the lead twice before Washington made two baskets to help the Wildcats take a 62-56 lead midway through the second half.
Kentucky went cold and LSU took advantage with a run that gave it a 65-64 lead on Reath's 3-pointer with 3:33 left.
Washington's three-point play gave the Wildcats a two-point lead before Reath's dunk pulled the Tigers even.
Back-to-back layups by Washington and Alexander gave Kentucky a four-point lead with a minute left.
Waters' jumper cut the lead to two before Wenyen Gabriel made one of two free throws.
Epps' jumper got LSU within one, but Gilgeous-Alexander made two free throws to give Kentucky a 74-71 lead with 16 seconds left.
Waters missed a 3-pointer, the rebound went out of bounds to LSU with 0.8 seconds left and Brandon Sampson missed another 3-pointer at the buzzer..
Kentucky scored the first seven points of the game, but LSU fought back and took its first lead, 20-18, on Waters' layup midway through the first half.
The Wildcats briefly regained the lead before Epps' layup put the Tigers back on top, 27-25.
The teams kept trading baskets until Epps made a 3-pointer that gave LSU a 36-31 halftime lead.
--Field Level Media
Kentucky | Louisiana State | |
Shai Gilgeous-Alexander 18 | Scoring | Duop Reath 24 |
Shai Gilgeous-Alexander 4 | Assists | Brandon Sampson 4 |
Kevin Knox 11 | Rebounds | Duop Reath 11 |
Shai Gilgeous-Alexander 3 | Free Throws Made | Tremont Waters 4 |
Wenyen Gabriel 3 | Steals | Skylar Mays 2 |
PJ Washington 2 | Blocks | Aaron Epps 2 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Kentucky | 74 | 50.8 | 5-12 | 7-13 | 13 | 34 | 3 | 6 | 14 |
Louisiana State | 71 | 44.6 | 6-24 | 7-9 | 14 | 32 | 5 | 6 | 11 |