Warren scored both of his touchdowns in the second half as the Tigers (4-3, 2-2 Southwestern Athletic Conference) rallied from a 12-7 halftime deficit with 16 second-half points.
Warren's 1-yard run gave Grambling a 13-12 lead with 10:21 left in the third quarter.
Ari Johnson kicked a 20-yard field goal for a 16-12 lead before Warren scored on a 40-yard run with 1:51 left in the fourth quarter to put the game out of reach.
Chris Mitchell was 14 of 29 for 192 yards and threw a 16-yard touchdown pass to Robert Childers that capped a 12-play, 93-yard drive and gave Alabama State (3-3, 0-3) a 12-7 lead with 41 seconds left in the first half.
Grambling sacked Mitchell five times and intercepted two of his passes.