Following a lively first half, Oman sought to apply pressure after the break, the midfielder Salaah Al-Yahyaei prodding away at the Thai defence but finding no way through.
At the other end, Buriram United striker Supachai Chaided - who scored a brace in Thailand's opening 2-0 win over Kyrgyzstan - cut an increasingly isolated figure.
Thailand appeared content with a draw, which leaves them top of Group F on four points after two games and with a good chance of progressing to the last 16.
Saudi Arabia are second on three points but have a game in hand, against Kyrgyzstan later Sunday. Oman have one point and Kyrgyzstan none. The top two are guaranteed to reach the next phase, but third place could also be enough.