Marquel added 13 points and Cooper had 10 points and grabbed 11 rebounds for the Monarchs (1-1). Breon Key also had 10 points for Old Dominion.
The Monarchs sank just 8 of 18 free throws (44.4 percent) but hit 9 of 23 from long range (39.1 percent) to get a win in the first round of the Naismith Memorial Hall of Fame Tipoff.
The Blackbirds (0-2) led 32-30 with 5:06 left in the opening half, but Cooper hit a jumper and dropped in a layup to spark a 9-0 run for a seven point lead at the break. Old Dominion never trailed again, and outscored Long Island 38-37 in the second half to seal it.
Michael Culpo scored 15 points to lead Long Island.