The Qatari side, featuring many players expected to represent the tiny gulf state at their home 2022 World Cup, looked set to secure the Olympic berth when they led 1-0 but Muhanad Abdulraheem equalised for the Iraqis in the 86th minute.
Substitute Aymen Hussein then sealed victory with a header four minutes into the second period of extra time to send Iraq back to the Olympics for the first time since losing the bronze medal match to Italy at the Athens Games in 2004.
"This victory really is the fruit of the great work of the Olympic committee in Iraq since we started our preparation," said Iraq assistant coach Hayder Najem.
The final of the under-23 tournament takes place later on Saturday between Japan, who beat Iraq 2-1 after a 93rd minute winner in the semi-finals, and South Korea.
Both East Asian sides will also represent the continent at the Aug. 5-21 Games in Brazil.
(Writing by Patrick Johnston in Singapore; Editing by John O'Brien)
