The Wildcats (1-1) went up 10-0 in the first quarter on a field goal by Adan Olivares and a 56-yard interception return by Ira Jewitt.
From then on, it was all Alcorn State.
Haiden McCraney began the Braves' scoring run with a 35-yard field goal late in the first quarter. Alcorn State led 24-10 at halftime.
Easton Melancon was 18 of 34 for 136 yards passing for the Wildcats.
The game marked the first meeting between the two teams and the first time Louisiana College has faced a Division I opponent.