Jordan will meet South Korea in the first semifinal on Tuesday, January 6 while Iran will play defending champions Qatar on Wednesday, January 7.
Jordan, who will appear in the semifinals for the first time, booked their spot with a hard-fought 1-0 win over debutants Tajikistan on Friday.
South Korea, seeking a third AFC Asian Cup title but their first since 1960, had to work even harder, needing extra-time to edge Australia 2-1 with Son Heung-min scoring the winner with a spectacular free-kick.
Defending champions Qatar checked in after defeating Uzbekistan 3-2 on penalties after their last eight tie ended 1-1 after 120 minutes at the Al Bayt Stadium.
Iran, who advanced earlier on Saturday, defeated Japan 2-1 in a quarter-final meeting between two sides who have lifted the AFC Asian Cup trophy seven times between them.
The final will be played on Saturday, January 10.