Smith also hauled down seven rebounds and handed out six assists for the Blue Devils (16-1, 3-1 ACC), who recovered from their first loss of the season Wednesday against Florida State to register their 30th straight home victory.
Andre Dawkins scored 14 points, Kyle Singler added 13 and Mason Plumlee grabbed 16 rebounds for the victors.
The Cavaliers (10-7, 1-2), meanwhile, lost for the 14th straight time on Duke's home court.
Mustapha Farrakhan and Joe Harris put in 15 points apiece for Virginia.
Celebrity Families of 2014 [PHOTOS]