Nam spent about an hour and a half to defeat Zhou Sheng Hao of China 6-4, 6-2.
He will next play the winner of the match between Zhang Zhizhen of China and Rhett Purcell of Great Britain.
Nam also marked another milestone in his career when he ranked No 475 in the world on July 3, the highest that a Vietnamese player has achieved so far.
Nam, 20, is one of the top 32 players in Asia and No 2 in Southeast Asia.
Among the other Vietnamese players, Trinh Linh Giang is ranked 1,351, and Nguyen Hoang Thien is placed 1,472 in the men’s singles category.
In the men’s doubles category, Nam stays at 503 and Thien is at 752.