Anthony Gill had 19 points to pace the Hoos, and London Perrantes added all 12 of his points on 4-of-8 shooting from beyond the arc. Virginia hit 12 three-pointers in all, its highest ever in an NCAA Tournament game.
Quinton Chievous led Hampton with 17 points.
The game's scariest moment came at the end of the first half, when Virginia coach Tony Bennett appeared to lose consciousness for a moment on the sidelines. He was taken to the locker room with five seconds left in the first half, but returned in the second, saying he had gotten dehydrated and stood up too quickly.
Virginia advances to face Butler on Saturday. The 9th seeded Bulldogs knocked off Texas Tech, 71-61.