Iliadis shot 53.8 percent from the field (7 of 13), 45.5 percent from 3-point range (5 of 11) and made all three of his foul shots.
Cooper scored 12 points and grabbed 16 rebounds, including eight on the offensive end.
Old Dominion entered the second half trailing 30-22 but outscored James Madison (7-5, 1-1 Colonial Athletic Association) 31-23 during the period as Kent Bozeman's jumper with six seconds left sent the game into overtime.
The Monarchs (7-7, 2-0) made eight free throws in overtime and held the Dukes to just two buckets over the final three minutes.
Humpty Hitchens led James Madison with 23 points but turned the ball over three times in overtime and shot 25 percent (1 of 4) during the period.