The 21-year-old athlete received 14,600 points after delivering an impressive performance.
China's Lan Xingyu won the gold with 15,433 points while Japan's Tanigawa Wataru finished third with 14,300 points.
Previously, Phong earned a gold medal at the 32nd Southeast Asian Games (SEA Games 32) in Cambodia in May after he beat world champion Carlos Yulo of the Philippines.
It was the first medal for the gymnastics squad at ASIAD 2023.
Earlier on the same day, shooter Pham Quang Huy won the first gold medal for Vietnam after scoring 240.5 points in the men's 10m air pistol event. Vietnamese shooters also won a bronze in the men's 10m air pistol team event with 1,730 points.
Vietnamese athletes are aiming to achieve 2-5 gold medals at ASIAD 19 which is close to its achievement at ASIAD 18 in Indonesia in 2018, which is the most successful Asian Games of Vietnam to date with five golds in women's rowing, athletics, women’s long jump, men's pencak silat, and women’s 400m hurdles.
