The Asian team had the better of the chances in the opening minutes, but the African side soon started to control the game and took the lead after 27 minutes, Hassan Ahmed finding the target from a free kick.
However, Egypt's lead was short-lived as Ammar Abdulhussein managed to squeeze the ball in from close range just five minutes later to ensure that the sides headed into half time level.
The referee was kept busy after the break as the pressure of trying to find a winner started to get to players on both sides, resulting in a number of bookings.
Mohamed Samir had a good chance to restore Egypt's lead, but it was the Iraqis who managed to find the third goal when Mohanad Abdulraheem coolly slotted the ball in with just over 10 minutes to play.
The result lifts Iraq above Chile on goal difference in Group E.