Stephen F.Austin 31, Nicholls St. 27
Moses was 36-of-47 for 366 yards and four touchdowns for the Lumberjacks (7-2, 4-1 Southland Conference).
Nicholls State (1-8, 0-5) was led by Marlin Meeks' 144 yards and a touchdown on 16 rushing attempts but was held scoreless after leading 27-21 at halftime.
The winning score culminated a seven-play, 61-yard drive for Stephen F. Austin in which Moses completed all five pass attempts.
Brooks' eight receptions (for 59 yards) tied for a team high. Contrevious Parks had 111 yards on six catches.
Quarterback LaQuinton Caston ran and passed for scores for Nicholls State, but the Colonels were held to 122 yards in the second half.
Parks, Aaron Rhea and Tyrone Ross caught the other scoring passes from Moses.