Thao finished second in the women's category with a 6.3m jump, while Mayookha Johny dominated the category from the outset and finished on top of the podium with a leap of 6.35m, an effort that propelled her to India's first Asian indoor title in the event.
Olga Rypakova of Kazakhstan finished third, recording a jump of 6.22m.
Thao's jump wasn't enough to earn her a ticket to compete in the 2016 Summer Olympics in Rio de Janeiro, Brazil as the qualifying result is 6.70m.
Thao's best performance was in the 28th Southeast Asian Games in Singapore last year with a 6.65m jump won a silver medal. She also won silver at the Asian Games in 2014 with a 6.44m jump.
Another Vietnamese representative, Quach Thi Lan brought home a bronze medal in the women's 400m with a time of 55.69 seconds, behind Oluwakemi Mujidat Adekoya of Bahrain at 51.67sec, and Elina Mikhina of Kazakhstan at 53.85sec.
Lan, from the northern province of Thanh Hoa, failed to qualify for Brazil as her time didn't meet the Olympic standard of 52.20sec.
20-year-old Lan said she wasn't satisfied with her performance. She added that she had recently recorded a time of 54.48sec at a tournament in the US.
Vietnam's two other competing athletes, Quach Cong Lich and Tran Hue Hoa, also fared poorly in the men's 400m and women's triple jump.
Lich and Lan are currently training in the US. After the Asian championships, they will return to the US to continue their training.
Nearly 300 athletes from 36 countries took part in the three-day tournament in the same facility that hosted the event in 2008 and the IAAF World Indoor Championships two years later.
Vietnam secured two places in athletics events for the London Olympics in 2012 at the last world indoor championships, but failed to secure any places this year.
