A 3-pointer by Singletary with 6 seconds left tied the score at 75. Singletary then hit a layup and hit a free throw after a steal with 4 seconds remaining to give Virginia the lead for good at 78-75.
Old Dominion (18-16) had a chance to come back with 3 seconds left after Jonathan Adams made a free throw to cut Virginia's lead to 78-76.
But Adams turned the ball over, and Ben Finney fouled Virginia's Calvin Baker. Baker hit two free throws to seal the win.
Singletary scored 22 points, Mamadi Diane had 14 and Jamil Tucker added 11 for Virginia.
Brian Henderson led Old Dominion with 26 points.
Virginia battled back from a 37-29 halftime deficit.