Aggies running back Kendall Bussey scored the go-ahead touchdown with a 2-yard plunge with 7:34 left in the fourth quarter.
Texas A&M (1-1) was responding to Nicholls State's tying score early in the period.
Colonels quarterback Chase Fourcade threw a 5-yard touchdown pass to wide receiver Stephen LeBouef to cap a four-play, 66-yard drive with 12:05 remaining.
Bussey led Texas A&M with 97 rushing yards on 15 carries. He carried nine times for 47 yards as the Aggies ran six minutes off the clock late in the fourth quarter.
Kicker Daniel LaCamera booted a 26-yard field goal for Texas A&M's final points with 27 seconds left.
Texas A&M staked an early two-touchdown lead on the strength of veteran ball carriers.
Aggies wide receiver Christian Kirk got wide open behind the Nicholls State defense and hauled in a 27-yard touchdown pass from quarterback Kellen Mond to cap Texas A&M's game-opening offensive series. Kirk's touchdown gave the Aggies a 7-0 lead with 11:39 left in the first quarter.
Texas A&M running back Trayveon Williams ran 17 yards for the Aggies' second touchdown in the opening quarter. Williams' TD finished an eight-play, 81-yard scoring drive.
But the Aggies' inconsistency on offense showed up in the second quarter as Nicholls State shut out Texas A&M in the period and chipped away at the lead.
Nicholls State kicker Lorran Fonseca booted field goals of 37 and 34 yards as the Colonels began to find some offensive rhythm in the second quarter.
Fourcade completed 5 of 10 passes in the second quarter for 80 yards, leading the way as the Colonels outgained Texas A&M 96-13 in total offense in the second.
Mond connected on just 2 of 8 passes for 11 yards in the second quarter as the Aggies failed to build on their first-quarter momentum.