Competing over two rounds on February 17-18, the trio delivered a strong performance, finishing with a total of 1,727 points to take gold.
Japan took a silver with 1,714 points, while Indonesia earned a bronze with 1,711 points.
Earlier, Vietnam won a gold in the mixed 10m air pistol event on February 12.
The Asian Rifle/Pistol Cup 2025 is taking place in Thailand from February 9-22, featuring over 280 top marksmen from 23 countries and territories.
Vietnam has sent an 18-member squad to the competition.
