Five players reached double figures for North Carolina State (3-2), which led by 12 early in the second half. Barber scored six of his points in overtime when the Wolfpack outscored the Tigers by an 18-7 margin.
Caleb Martin scored 16, Malik Abdul-Abu added 15 while Cody Martin and Maverick Rowan had 14 and 10 respectively.
LSU (3-2) star freshman Ben Simmons fouled out early in overtime but had his fourth double-double. He finished with 14 rebounds and 10 assists but missed his first five shots before hitting a game-tying layup with 38 seconds remaining in regulation. Tim Quarterman led the Tigers with 19 points and Brandon Sampson added 18.
Abdul-Abu nearly gave the Wolfpack the win in regulation with seven seconds remaining but his basket was taken away after officials determined a shot clock violation had been committed.
On North Carolina State's first possession of overtime, he drove to the basket and gave the Wolfpack a lead they did not relinquish, though it was not easy.
LSU was within 73-72 on a 3-pointer by Sampson with 1:50 remaining but nearly a minute late, Cody Martin drove for a layup and a 75-72 edge. After Tim Quarterman missed a layup, Rowan converted a layup with 38 seconds remaining.
LSU forged a 65-65 tie when Simmons was fouled on a layup with 38 seconds remaining. Simmons missed the subsequent foul shot, giving North Carolina State a chance to regain the lead.
The Wolfpack were unable to as Abu's basket came after the shot clock expired. Abu was originally credited with the basket but following a review the call was changed.
LSU called a 30-second timeout with 4.2 seconds remaining and Blakeney was fouled with 1.9 seconds remaining since North Carolina but was unable to hit the game-winning 3-pointer before time expired.
LSU: Sampson came off the bench for the first time after shooting 32.4 percent (12-of-37) in his first four games. He was replaced in the starting lineup by Jalyn Patterson, who had shot 21 percent (6-of-17) in the first four games. ... In Monday's loss to Marquette, Simmons was the eighth player since 1973-74 to collect at least 20 points and 20 rebounds and his performance was the 13th by a Tiger.
North Carolina State: Tuesday was a rematch of last year's NCAA second round tournament game, which the Wolfpack won by a 66-65 margin. LSU led by 14 at halftime and NC State's defense held the Tigers to 29.2 percent shooting in the second half while BeeJay Anya hit the game-winning shot with one-tenth of a second remaining. ... Caleb Martin was shaken up briefly with about six minutes remaining in the first half when he took an elbow to the face by LSU center Elbert Robinson III. Martin stayed in the game and hit a 3-pointer a few possessions later
LSU: at Charleston on Monday
North Carolina State: Winthrop on Friday