Second-half goals to Massimo Luongo and Tomi Juric on Thursday night ensured the right result for the Socceroos on an evening that almost threatened to end sourly.
A first half of frustration gave way just before the hour mark, when Luongo arrived on the spot to thrash home Juric's squared ball.
The striker made sure of the result on 65 minutes, when Mark Milligan successfully drew attention from Aaron Mooy's corner, allowing Juric to tap home from a metre.
The result - if not the performance - will please Postecoglou, who spoke of the importance of winning home games during this decisive qualifying group stage.
Sterner tests await, including the United Arab Emirates next Tuesday in scorching Abu Dhabi heat.
But with a shot count of 20-6 and 72 per cent of possession, the Socceroos can be content to avoid a banana peel during the first of 10 qualifiers leading to the 2018 tournament.
Australia were denied twice by the woodwork before cutting through, and allowed simple errors to creep into their play, almost in exasperation.
On 26 minutes, Mathew Leckie's majestic long-range header reduced goalkeeper Mohammed Hameed to a bystander, only to bounce off the inside of the post and away.
Mile Jedinak, who was uncharacteristically astray in his passing, headed Mooy's cross just over.
At halftime, it felt like the Socceroos had control of the play, but not the contest.
Improved intensity after the break soon had the Iraqis swamped.
A fine move between Jedinak and Mathew Leckie ended with Mooy crashing an effort onto the bar.
Australia had their swagger back, and a breakthrough seemed inevitable.
