The 21-year-old defeated powerful Yeom Hyejeong of the Republic of Korea in the women's individual recurve event 26-26, 27-26, 28-25, 28-28.
Li Tsai-chi of Chinese Taipei earned a bronze.
Earlier, in a group with teammates Do Thi Anh Nguyet and Ha Thi Ngoc, Nhi also grabbed a bronze in the team recurve event, beating India 47-50, 51-46, 55-49, 51-47.
Chinese Taipei took the gold and the RoK claimed the silver.
It was Nhi's third international tournament in her career. Earlier, she took part in the 31st SEA Games in May in Hanoi where she earned a silver in the women's team recurve. Four months later, she grabbed two golds in both individual and team recurve events at the Singapore Open.
In Sharjah, Vietnamese athletes also competed in the compound events but none of them could advance to the top three. Their best result was fourth place in the men's compound team, losing 55-58, 58-56, 52-55, 56-58 to Bangladesh in the third-place playoff.
The Asia Cup was held from December 22-25 with the participation of 270 athletes from 31 countries.