Beckham hauled in a 33-yard scoring pass from Zach Mettenberger on the first play of the fourth quarter with LSU clinging to a 31-26 lead, igniting a 28-point outburst to end the game.
The Tigers (5-1, 2-1 SEC) iced it when Tre'Davious White picked off Mississippi State quarterback Dak Prescott, returning the ball to the Bulldogs' 5-yard line, and Jeremy Hill then ran it in for another score.
Mettenberger completed 25-of-29 for 340 yards with two touchdowns and an interception.
The Bulldogs (2-3, 0-2) were led by Jameon Lewis with seven receptions for 111 yards and a score.
Celebrity Families of 2014 [PHOTOS]