The consecutive punt returns and a 20-yard TD run by Courtney Brown one minute into the game staked Prairie View (6-2, 6-1 Southwest Athletic) to a 19-0 lead, which grew to 40-14 by halftime.
In the second quarter, the Aggies scored three-straight rushing touchdowns - Anderson from the 7, Johnta Hebert's 61-yarder on first down, and DeAuntre Smiley from the 3.
Alcorn State (5-3, 4-2) cut the gap to 19-14 on TD runs of 36 and 52 yards by Lenorris Footman. Footman rushed for 220 yards and passed for another 143 with two more touchdowns. Footman broke the Alcorn State and SWAC single-game rushing records a week earlier at Southern.
The Braves remain atop the SWAC East Division while Prairie View remains just behind unbeaten Grambling (7-0) in the West.