Darrel Mitchell scored 18 points on six 3-pointers for LSU, which has lost five of its last six entering next week's SEC tournament.
LSU's last lead came with 8:07 left in the first half, but the Tigers pulled within one point on a 3-pointer by Mitchell.
From there, Robinson took over. He scored eight points during a 13-3 spurt that put Auburn ahead 72-61.
Mitchell responded with another 3, but Robinson hit another basket to put Auburn ahead by double-digits for good.
With 24 seconds to go on Senior Day, Auburn's four seniors took the Beard-Eaves Coliseum court likely for the final time. Kyle Davis, the school's all-time shot blocker, capped the day with a 3-pointer.
Young had 11 points in a seesaw first half. Auburn built its biggest lead at 39-32 on a Lewis Monroe layup with 2:32 left in the half, but LSU scored five in a row and trailed 42-39 at the break.