The Tigers improved to 32-7 overall and took over sole possession of first place in the SEC standings with a 12-4 mark. Kentucky is 33-6 overall and 11-5 in league play.
The series resumes at 1 p.m. Saturday as sophomore right-hander Ryan Eades will start on the mound for LSU. Kentucky will counter with junior left-hander Jerad Grundy.
With Friday's win, the Tigers are now 8-2 this season in SEC games decided by one run.
"What a great game, and I'm extremely proud of our players for earning the win (Friday)," LSU coach Paul Mainieri said. "Kevin Gausman gave us another courageous effort, and our bullpen was tremendous as it has been all season. Austin Nola has been a clutch hitter for us throughout his career, and he demonstrated that (Friday) with two big two-out hits.
"Kentucky has an outstanding club, but I thought our players showed a lot of determination and heart in getting this victory."
Gausman (7-1) threw 101 pitches in seven innings, allowing four runs on 10 hits with one walk and 11 strikeouts. Junior left-hander Chris Cotton pitched a perfect eighth inning and junior right-hander Nick Goody struck out the side in the ninth to secure his 6th save.
Kentucky starter Taylor Rogers (4-2) was charged with the loss as he surrendered five runs (three earned) on eight hits in six innings with two walks and four strikeouts.
LSU grabbed a 2-0 lead in the first inning against Rogers. Center fielder Arby Fields walked and was caught in a rundown when attempting to steal second, but he advanced safely when first baseman A.J. Reed made an errant throw.
Tigers left fielder Raph Rhymes grounded to second, where UK second baseman J.T. Riddle committed a throwing error, allowing Fields to score and Rhymes to move to second. Nola singled to score Rhymes with the second run of the inning.
The Wildcats narrowed the gap to 2-1 in the second when left fielder Zac Zellers delivered a one-out single and later scored on designated hitter Michael Williams' grounder to first base.
LSU increased its lead to 3-1 in the fourth on a solo homer by first baseman Tyler Moore, his second of the season and first to leave the ballpark.
Kentucky tied the game in the fourth on an RBI double by right fielder Cameron Flynn and a run-scoring single by Zellers.
The Tigers regained the lead 5-3 in the fifth on a two-out, two-run double by Nola, but Kentucky reduced the margin to 5-4 in the sixth on Williams' RBI single.
Gausman pitched a scoreless seventh before yielding the mound to Cotton to start the eighth inning. Cotton retired Flynn on a fly ball and Zellers on a groundout before fanning Riddle to end the frame.
Goody preserved the win in the ninth by striking out Williams, pinch hitter Jeff Boehm and centerfielder Austin Cousino to end the game. That was the fifth strikeout of the might for Cousino, the Cats' leadoff hitter.
Saturday's game is scheduled to be televised live by Fox College Sports Atlantic (Cox Cable Ch. 255). The game can also be heard on the affiliates of the LSU Sports Radio Network, and live audio and stats are available at www.LSUsports.net/live.