A great result more than it was a great performance, a job done rather than a job well done.
This was a great contest and a wonderful game, but history won't remember it as one of the Socceroos' most fluid recent performances as the Iraqis did more to lose the game then Pim Verbeek's men did to win it. We were lucky.
But for some wastefulness in front of goal from the likes of Hawar Mulla Mohammed, Younes Mahmoud and Emad Mohammed and a couple of strong moments from Schwarzer it might well have been the Iraqis with the momentum as Australia's campaign shifts to a fortnight in the heat of the Middle East.
As it is, the Socceroos now sit on seven points from three games, knowing that one more win will take them to 10 points, the figure Verbeek believes will get them over the first hurdle.
If and when they do get to the next phase, and face the likes of Saudi Arabia, Japan, South Korea, Iran and Uzbekistan, one thing's for certain; the performance, especially in the heart of the defence and the final third, will need to improve.
In many ways, this was very much a below strength side, especially in the two areas I mentioned above, and both areas will improve with the eventual return of new fathers Neill, Sterjovski and Kennedy.
Right from the start and contrary to the pre-game talk from Verbeek that Iraq had come to sit, Adnan Hamad's men exposed the insecurity and inexperience in the heart of the Roos defence, coming at Australia, pressing high, and creating some uncertainty, especially from set-pieces.
With the skipper putting himself about in the style we grew familiar with at the Asian Cup and Hawar, Emad and Mahdi Karim stretching Australia with their pace and width on the vast and patchy Suncorp pitch, it might have and should have been a different story.
Emad was unlucky to hit the cross-bar early, before finding himself inside the box, unmarked midway through the first period after some poor defensive work from Carney and Beauchamp (Carney let his man Karim duck inside, Beauchamp went across to rescue and left his man, Emad, unmarked). Fortunately, they were rescued by Schwarzer, who stayed up as long as possible.
Later in the half, Mahmoud failed to hit the target with a free header, six or seven yards out. Australia was leading a charmed life in making it six clean sheets on the trot.
In and around that, the Socceroos had a couple of chances, the best falling to Mark Bresciano after some lovely interchange between he, Kewell and McDonald. In truth, that early move was one of Australia's best moments in the game.
Kewell, after a disappointing performance against Ghana a week ago, was back to his exhilarating best, his touch, movement and leap proving too slick for the likes of Haider and Ali Rahema. He looked trim (who didn't in the new-look fitted strip, a flattering one for the players, not so flattering on most of us fans), young and fresh.
Having seen some highlights of him burning Zadkovich in training on Thursday evening, it wasn't a great surprise to see him doing so well here. You sensed he was in the mood.
After warming up with a couple of headers in the first period, his bullet early in the second, teed up by Wilkshire, was a reminder that, on his day, there hasn't been a better player in the green and gold, ever.
The hope now is that his body can hold up over the next two years, especially throughout the crucial games that a sure to come in the next phase. But would you bet on it?
One thing that appears more certain is that the Socceroos, with the likes of Grella, Culina and Wilkshire in midfield, and Emerton chiming in from right back, will continue to control possession well. Certainly, the Socceroos did a far better job of controlling the midfield (in the process nullifying the threat of the Asian Cup nemesis Nashat Akram) than they did against Ghana.
Problem was, for all their neat ball-possession, there wasn't enough forward support of Kewell and McDonald. Cahill was definitely missed.
But perhaps not as much as Neill. Often the space between the defensive line and the attack was far too spacious, and the midfield had acres to cover.
Hitherto Jade North has looked extremely comfortable alongside Neill, but here he had the responsibility to organise, and it was a task he probably wasn't ready for, especially against such quality opposition. I thought the Jets skipper played well, especially in second period, cleaning up a number of Beauchamp bloopers, but he will need more time alongside Neill to develop into the composed "boss" that is required at this level.
Carney also needs games and time and was again caught out a couple of times as Iraq got in behind and ducked inside, but he made up for them with a couple of timely interventions.
In the second period, the Socceroos were again lucky to survive a couple of Emad and Mahmoud efforts, but Iraq's best chance came late when Hawar beat the offside trap, only to have the ball hold up a touch, forcing him to volley straight at Schwarzer.
Verbeek by then had introduced the likes of Holman and Djite, the latter doing a couple of good things, including teeing up a chance for Holman, who shot wide.
Overall, this was far from an impressive performance, lucky even, but in the context of what's required to get through this phase, is should be enough.
If Qatar and China draw on Tuesday morning our time, Iraq will be only three points from second, and still in with a sniff, but a win, to either side, will make it much much harder for the troubled Asian Championships.
As Verbeek said post-match, knowing Iraq, they will fight to the end, so a tough trip to Dubai awaits.