LSU (18-14) never let the Wildcats take control of the game but Kentucky (31-1) still came through with its 23rd consecutive win.
The Wildcats will next face No. 19 Florida, which earned a semifinal berth by edging Alabama 66-63.
Mississippi and Vanderbilt will tangle in Saturday's second semifinal game. Mississippi surprised second-seeded Tennessee in the quarterfinals with a 77-72 overtime victory and Vanderbilt overwhelmed Georgia 63-41.
Jones had a 5-0 run that put Kentucky up 39-35 with 12:10 to go and the Wildcats managed to lead by as many as nine. LSU then faltered down the stretch, failing to hit a field goal after Andre Stringer's jump shot with 4:31 to go.
Davis had 12 points, 14 rebounds and six blocked shots. Jones finished with 15 points and 11 rebounds. Michael Kidd-Gilchrist was one rebound short of a double-double and had a game-high 19 points.
LSU, which shot just 29.4 percent, was led by Storm Warren with 14 points.
Alabama's JaMychal Green had three field goals and an assist on a 3-point basket from Trevor Lacey that got the Crimson Tide within 64-63 with 21 seconds to go against Florida.
The Gators' Kenny Boynton then made two free throws and a desperation 3-point try by Alabama went off the rim. Florida will take a 23-9 record into its meeting with Kentucky. Alabama dropped to 21-11.
Bradley Beal had 16 points, Erik Murphy 15 and Boynton 14 for the Gators. Green had 22 points and 10 rebounds.
Mississippi missed a chance to defeat Tennessee in regulation when the Volunteers' Skylar McBee hit a game-tying 3-pointer with 3 seconds left.
The Rebels, however, held Tennessee scoreless for the first 4:07 of the extra period while building a seven-point lead. Mississippi (20-12) received 19 points from Terrance Henry and held Tennessee to 28 percent shooting.
Trae Golden had 21 points for the Volunteers (18-14).
Vanderbilt (22-10) held Georgia to just 16 points in the second half to set up its meeting with Mississippi. John Jenkins had 15 points for the Commodores.
Dustin Ware, with 10 points, was the only player in double figures for the Bulldogs (15-17).
Attkisson leaves CBS News, reportedly over network's 'liberal bias'
LGBT community has 'bullied the American people': Bachmann