Reno Piscopo scored a stunning free-kick to give Australia the lead just after the hour mark, before Mohammad Qasem found the net to earn Iraq a point at Thammasat Stadium.
After a scoreless first half, Wellington Phoenix winger Piscopo found the top corner with a powerful strike after being tripped by Mohammed Ridha Jalil 30 yards from goal.
Iraq substitute Qasem then came off the bench to rescue a point.
Eight minutes after his introduction, Qasem rode a tackle before curling a superb strike past the diving Thomas Glover, finding the bottom corner via the inside of the post in the 77th minute.
The Olyroos almost grabbed a late winner, but defender Dylan Ryan’s glancing header came back off the post.
“This goal, I dedicate it to the families back home in Australia, the victims, so it was special for me,” Piscopo said afterwards.
A moment’s silence was held prior to kick off in memory of those affected by the fires in Australia.
Hosts Thailand thumped Bahrain 5-0 in Group A’s other match.
Next up for the Olyroos is a clash against Thailand on Sunday (AEDT) at Rajamangala Stadium.
The top two teams from the four groups will advance to the quarter-finals.
Olympic qualification for the first time since 2008 is on the agenda for Graham Arnold’s side, with the tournament’s top three teams set to join Olympic hosts Japan at Tokyo 2020, meaning the two finalists and the third-place play-off winner all qualify.