Stroud tied a school record with his five touchdowns tosses.
The McNeese State Cowboys (3-0) were trailing 35-31 as the fourth quarter began. Stroud engineered an 82-yard drive, culminating in a 28-yard pass to Jereon McGilvery to put them in front 38-35. The West Alabama Tigers (1-1) marched right back to retake the lead, 42-38, with 3:41 remaining in the game on Gary Johnston's 2-yard run.
Stroud, who totaled 366 yards passing, completed five passes as he led the Cowboys 66 yards for the final score.
West Alabama failed to get past their own 24 yard line as the Cowboys sealed the game.
Kyle Caldwell led the Tigers, throwing for three touchdowns and 300 yards.