The Monarchs (7-2) started the game with an 18-0 run and maintained a double-digit lead the rest of the way.
The Hawks (2-6) did not make their first basket until a Lyvann Obame Obame layup with 12:36 to go in the first half.
Old Dominion outrebounded the Hawks 64-28, setting a Ted Constant Center record for most rebounds, and scored 24 second-chance points.
Keyon Carter added 13 points and nine rebounds for the Monarchs and Chris Cooper tied the arena record with a career-high 16 rebounds. Old Dominion's Alex Loughton also had 16 against George Mason in 2004.
Obame Obame and Dishawn Bradshaw scored eight points each for Maryland-Eastern Shore, which shot only 25.9 percent from the field (15 of 58).