Alcorn State scored on a 7-yard run by John Gibbs Jr. but Haiden McCraney's PAT kick was blocked.
The game was a meeting of the Southwest Athletic Conference's unbeaten teams. Grambling (5-2, 5-0) tops the SWAC West. Alcorn State (4-2, 3-1) still leads the East.
Carter had his second-straight 100-yard game, rushing for 133 yards on 11 carries.
Gibbs rushed for 96 yards and two TDs, and passed for 222 yards with another score as Alcorn State scored four touchdowns to lead 28-14 at halftime. Grambling scored twice in the third quarter to tile 28-28.
Alcorn State gained 218 yards on the ground with rushing touchdowns from Gibbs, Aaron Baker and Darryl Ragsdale