Vietnam entered the game with confidence and created more chances, but some lacked accuracy while others were saved excellently by keeper Al-Mukhaini.
Oman's Khalid Al-Hajri scored the game's only goal by heading the ball in from a corner in the 64th minute.
Vietnam had asked for a penalty after the ball hit the hand of an Oman defender in the 57th minute, but referee Hanna Hattab decided against it after checking with the VAR room.
Both Vietnam and Oman have no chance left to qualify for the 2022 World Cup, but the Thursday result affects their group standing. The victory allows Oman to retain their fourth position, while Vietnam are still at the bottom, after China.
In the same group, Japan's 2-0 victory over Australia on Thursday sent them to the seventh successive edition of the World Cup finals. The victory also secured Saudi Arabia's passage to Qatar while third-place Australia will have to go through two playoffs.
Vietnam will play Japan next on Tuesday.