Wu, a 24-year-old competing in his first Olympics, won Brazil its first medal of the Games, on the first day of competition, and its first in shooting since 1920.
He and the 41-year-old Hoang took turns at the top before the Vietnamese eked out a 0.4 of a point advantage to win with 202.5 points in 20 shots. Both are members of their countries' armed forces.
"In the last shot, all I was trying to do was finish it off," said Hoang, a two-time Olympian who also won his country's first medal in shooting.
China's Pang Wei, who won the gold medal in Beijing in 2008, took the bronze, while defending Olympic champion Jin Jong-oh of South Korea failed to recover from a poor start and finished fifth.
On the first day at the Deodoro Shooting Centre, the mostly Brazilian crowd whooped and whistled the national anthem for Wu and created quite a bit of noise at crucial moments of the competition.
Wu said he was not bothered by it.
"It is just perfect," Wu said of his conquest for Brazil. "I hope that the sport of shooting becomes more popular in Brazil."
He also noted the difficulties of training in Brazil, a country in the midst of its worst economic crisis in decades, and the high cost and long delay associated with importing ammunition.
"Sometimes I have to wait for a year to get my ammunition," Wu said.
(Editing by Ed Osmond and Toby Davis)
