Mahmoud Saber gave Egypt an early lead just five minutes into the Group G match at Seattle Stadium in Seattle, United States.
Iran were awarded a penalty five minutes later, but Egyptian goalkeeper Mostafa Shobeir denied Mehdi Taremi from the spot.
Ramin Rezaeian leveled the score in the 14th minute after Shobeir failed to keep out Milad Mohammadi's powerful strike.
Iran almost secured a dramatic place in stoppage time when Shoja Khalilzadeh found the net, but the goal was ruled out for offside.
Iran had opened their campaign with a 2-2 draw against New Zealand before being held to a goalless draw by Belgium.
In the other Group G fixture, Belgium thrashed New Zealand 5-1 to finish top of the group with five points.
Egypt also ended the group stage with five points, advancing to the knockout stage as runners-up.
The draw kept Iran’s hopes of reaching the knockout stage alive.