Smith scored after stripping the ball from Marcus Thornton after an inbounds pass and raced down court for an easy score that decided the low-scoring affair.
Chris Johnson had 17 points, eight rebounds and four blocks, and Marcus Thornton 12 points and seven rebounds for the Tigers (8-15, 1-8), who have lost 10 of their last 11 games.
Tennessee held a 42-32 lead before LSU went on a 13-3 run to tie the game at 45-45 with 1:15 to play.
Caroline Berg Eriksen: Soccer player's wife triggers debate with post-birth selfie
Britney Spears on kissing Ryan Gosling, Justin Timberlake in the Mickey Mouse Club