George was 20-for-31 for 233 yards with scoring passes of 27 yards to Da'Marcus Griggs, 10 yards to Wood McClendon and 6 yards to Daren Dillard.
Karrington Bush rushed for a season-high 163 yards on 20 carries with one touchdown for Texas State, which scored off three Colonels fumbles.
The Bobcats (3-3, 1-1 Southland Conference) used a 21-point second quarter to lead 24-7 en route to their first victory in Thibodaux since 1999.
LaQuintin Caston ran for touchdowns of 11 yards and 1 yard and threw a 27-yard touchdown pass -- the Colonels' second passing score of the season -- for Nicholls State (1-5, 0-2).
A.J. Williams added 119 yards on 11 carries, including a 70-yard run, and scored on a 10-yard run with 2:41 left. The Bobcats then ran out the clock.