FIU (5-4, 3-3 Conference USA), which had won three consecutive games before being upset by Middle Tennessee 50-17 last week, led 16-7 going into the fourth quarter.
Morgan ran in from the 1 to go up 24-10 with 6:17 remaining in the game. Old Dominion marched 65 yards in 10 plays to close within a touchdown after Lala Davis scored from the 10 with 2:54 left.
The ensuing onside kick went out of bounds and FIU took over on ODU's 46. The Monarch defense stiffened, forcing a punt that gave the Monarchs the ball on their own 9. Two plays later Olin Cushion III picked off a Hayden Wolff pass to secure the win.
Jose Borregales had field goals of 21, 31 and 42 yards in the first half to give the Panthers a 9-7 lead at the break.
Wolff threw for 169 yards for Old Dominion (1-8, 0-5), which has dropped eight straight.
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