Shelley missed the extra point try on the only touchdown of the contest in New Orleans, a 34-yard TD run by Trent Richardson that closed out the scoring in the fourth quarter.
The Alabama (12-1, 7-1 SEC) defense limited LSU (13-1, 8-0) to a mere 92 total yards of offense and five first downs. The Tigers lost the ball twice on turnovers and quarterback Jordan Jefferson was 11-for-17 for 53 yards passing.
Alabama quarterback A.J. McCarron went 23-for-34 and threw for 234 yards. The Crimson tide rolled up 384 yards of total offense.
Richardson finished the game with 20 carries for 96 yards and also caught two passes for 11 yards.
LSU beat SEC rival Alabama in the regular season and entered the BCS title game undefeated.