Fields gave Louisiana-Lafayette (6-6, 4-4 Sun Belt) the lead for good in the first quarter when he threw an 18-yard touchdown pass to Chris Smith for a 7-3 lead with 5:35 left in the first quarter.
Seth Keller's second field goal pulled Texas State (4-8, 2-6) within 7-6 at the 10-minute mark of the second quarter. Kenneth Almendares sandwiched two field goals around freshman Dre'lyn Washington's 8-yard touchdown run in the final 5:38 to send the Ragin' Cajuns into the locker room up 20-6.
ULL went 61 yards in eight plays on its opening drive of the second half, scoring on Smith's 1-yard run for a 27-6 lead. Texas State's Lincoln Pare answered with a 64-yard touchdown run on the Bobcats' ensuing drive to cut their deficit to 14 after three quarters.
Fields' 3-yard touchdown pass to Peter LeBlanc made it 34-13 early in the final quarter. Freshman backup Zeon Chriss threw his first collegiate touchdown pass - a 37-yarder to Lance LaGendre to complete the scoring.
Fields connected on 16 of 26 passes for 187 yards with one interception for ULL. Chriss, who was 0-for-3 passing coming in, completed 5 of 6 for 84 yards.
Pare, a sophomore, finished with a career-high 221 yards on the ground, carrying 28 times. The rest of the Bobcats offense managed 135 yards.
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