Dung, aged nine, is a student of famed violinist Bui Cong Duy. Hung, 16, is a follower of artist Ngo Hoang Linh.
This is the third successive time Vietnamese students have won top prizes at the event.
The jury for the competition consists of distinguished musicians from around the world. They have previously served as jurors at other international competitions.
The biennial event designed for piano and violin was established to identify and encourage outstanding young musicians from the ASEAN region and to assist them by providing suitable performing opportunities.