Trang beat No 15 seed, Line Hojmark Kjaersfeldt of Denmark 21-19, 13-21, 21-11.
The Vietnamese player is world No 74, while Kjaersfeldt is world No 17.
Trang will face Yeo Jia Min of Singapore, who defeated world No 1 player Akane Yamaguchi of Japan, in the next round.
Earlier, Trang beat Kristin Kuuba of Estonia 21-12, 21-15 in the first round.
In the mixed doubles, Do Tuan Duc and Pham Nhu Thao lost to England’s Chris Adcock and Gabrielle Adcock 19-21, 10-21.
Trang is now the only Vietnamese representative still in the tournament, with all the other players eliminated, including the country's best male player Nguyen Tien Minh.
The tournament, which has attracted top players from 50 countries, will end on August 25.
