Bui Thi Ngan finished first in the women's 1,500m event with a time of 4min 29.75sec.
Tran Nhat Hoang won the men's 400m, clocking a time of 49.31sec.
Earlier, Pham Thi Hong Le grabbed a gold in the women's 10,000m after 39:04.52, and Vu Thi Ngoc Ha triumphed in the women's triple jump with a 13.30m attempt.
Vietnam has sent 53 athletes to compete at the Games, which will finish on August 6.
They are competing across track-and-field, taekwondo, pencak silat, Muay Thai, e-sports and futsal.