Georgia Southern led 15-0 before Texas State's second-half comeback.
Texas State got on the board with 59 seconds left in the third quarter. Keenen Brown ran for 61 yards before getting tripped up at the 4 and he punched it in on second-and-goal to pull to 15-7.
Jeremiah Haydel caught a 29-yard pass in the corner of the end zone to make it 15-13 with 2:20 left, but the Bobcats' 2-point conversion attempt fell incomplete. Georgia Southern recovered the onside kick and ran out the clock.
Fields powered in a 5-yard touchdown run to open the scoring in the second quarter for Georgia Southern (5-1, 3-0 Sun Belt), which has won four straight.
Freshman Tyler Vitt, who made his first start last week, threw for 132 yards with one touchdown and one interception for Texas State (1-5, 1-2).