Sulaimon connected of 4-of-5 from 3-point range en route to 21 points for the Blue Devils (13-4, 2-2 ACC), who blew a late 13-point lead but held on to avoid what would have a been a third loss in four games to begin conference play.
Amile Jefferson provided 10 points -- including a pair of free throws to seal the outcome -- and grabbed 15 rebounds.
Rodney Hood also reached double figures with 14 points.
Virginia (12-5, 3-1) was paced by Malcolm Brogdon, who netted 11 of his 17 points down the stretch to help spark the Cavaliers' rally.
Joe Harris supplied 15 points.