Victory for Iran earned a quarterfinal clash with China, which beat Thailand 2-1 in an early kickoff on Sunday.
And in the day’s first last-16 game, Vietnam edged past Jordan 4-2 on penalties after the teams were tied at 1-1 after extra-time.
Despite the exit, Pim Verbeek's Red Warriors can hold their heads high after some spirited performances throughout the tournament.
Three-time champions Iran was in for a shock as Oman’s striker Muhsen al Ghassani was brought down inside the box in the second-minute by Majid Hosseini only for the referee to point to the spot kick.
Captain Ahmed Mubarak 'Kanu' al Mahaijri took the penalty but his shot was brilliantly saved by Iran goalkeeper Alireza Beiranvand, who dived to his right correctly to deny Kanu.
Despite missing the golden opportunity to take a lead, Oman players did not lose their hearts and frustrated their rivals.
Iran, looking to end a 43 year old Asian Cup title drought, broke through after 32 minutes when Brighton forward Alireza Jahanbakhsh latched onto a long ball to poke the ball past Oman goalkeeper Faiz al Rusheidi after defender Mohammed al Musallami’s failed to cut Milad Mohammadi’s speculative cross.
Iran captain Ashkan Dejagah then lashed home a controversial penalty four minutes before the break after Saad Suhail was harshly punished for bringing Mehdi Taremi down.
Oman fought back and Beiranvand was forced to produce another acrobatic save to keep out Ghassani’s long-range strike just before the half-time whistle.
Iran could have extended its lead even further within eight minutes of the restart, but an unmarked Sardar Azmoun missed the target from 12 yards when Taremi’s long throw arrived at his feet.
Taremi then brought the best out of Oman custodian Rusheidi, while at the other end Harib al Saadi fizzed a 77th minute shot inches over Beiranvand’s bar. The 2018 Gulf Cup winner tried hard but failed to break through the Iran defence to bow out of a memorable tournament.
Elsewhere, in Al Ain, China mounted a second-half revival as it beat Thailand 2-1.
China was all at sea as it fell behind to Supachai Jaided's opener but it hit back after the break through substitute Xiao Zhi and Gao Lin's well-taken penalty.
And in Dubai, Vietnam emerged victorious from a penalty shootout against Jordan to become the first team to reach the quarterfinals on Sunday. After extra-time finished at 1-1, B T Dung rolled in the decisive spot-kick for a 4-2 penalties win after Baha Faisal and Ahmed Samir had missed for Jordan.