Steady rain throughout the day exacerbated what was already one of the worst pitches Australia has played on in recent years, and at times the new-look back three of Mark Milligan, Milos Degenek and Bailey Wright looked unable to cope.
Mooy's corner five minutes from the break superbly picked out Leckie, who headed home at the near post to relieve the pressure valve on the Socceroos.
It was only through some wasteful Iraqi finishing and some desperate defensive acts - such as Mark Milligan's last-second intervention to deny Amjed Kalaf a certain goal in the 22nd minute - that Australia was able to remain level until that point.
But the Lions of Mesopotamia kept on coming and in the 76th minute managed to square the ledger.
A terrific cross from Ali Adnan found Yasin, who scored to bring the small but vocal and largely pro-Iraqi crowd back to life in an instant.
Both teams had chances to win it in a frantic end to the match but it is undoubtably the Socceroos who will be happier with the point in th
