Georgia State (0-10, 0-5) got a late score in the first half as Ronnie Bell found Keith Rucker on a 42-yarder. Bell connected with Albert Wilson 22 yards for a game-tying touchdown in the third quarter.
Louisiana-Lafayette took the lead back on the next drive as McGuire scored on a 36-yard pass from Broadway.
Following a failed fourth-down conversion by Georgia State at the Louisiana-Lafayette 16, Broadway threw his fourth score to Jamal Robinson.
Georgia State's last two drives ended on failed fourth-down conversions, keeping them winless.