The contest featured six lead changes and neither team led by more than six points.
George's winning TD pass was his third of the game, and he also completed 27 of 39 passes for 301 yards for the Bobcats (6-3, 4-1 Southland). Daren Dillard caught nine passes for 147 yards and a score.
Brent Grimes had 166 rushing yards and two touchdowns for the Bears (5-4, 2-3). His second TD, which came on a 2-yard run, put Central Arkansas up 24-20 with 1:40 left.
The Bears' defense couldn't hold, though, and Texas State drove 50 yards on eight plays for the winning score.