Josip Skoko gave Australia the lead on just 15 minutes with a spectacular goal. After dominating the first half, the Socceroos then saw off a determined challenge from the visitors late in the match, to prevail in their first of three warm-up matches ahead of the World Cup.
Both defences took time to settle into the match, but despite some nervous moments, it took until the quarter hour mark for the first serious chance of the game.
The opening goal came from Australia's third corner of the night, with Lucas Neill heading back to Mile Sterjovski, who found Skoko. From just outside the box, he hit a well-timed volley into the top-left hand corner, leaving Antonios Nikopolidis stranded.
It set the crowd alight, and Australia made the better inroads in the next ten minutes. At the heart of it was Marco Bresciano, relishing his role in the five-man midfield. He almost doubled Australia's lead on 24 minutes when he took a 35-metre free kick which went just inches wide of the right post and soon after Sterjovski forced a save from Nikopolidis.
Greece was struggling to get strikers Angelos Charistaes and Georgios Samaras into the match, and when the ball was down Zeljko Kalac's end of the ground, Neill and Craig Moore were quick to cover.
A dangerous build-up from the Socceroos in the 39th minute could have resulted in a goal if not for a desperate headed clearance from Konstantinos Katsouranis, which got the ball away from Viduka. Two minutes later, the former Melbourne Knights player had claims for a penalty when his shirt was tugged at when he was through on goal, but English referee Mike Riley waved play on.
But the teams went to half time at 1-0, with the home fans wondering if it could have been a bigger advantage.
Greece made a raft of changes at the break, bringing captain Theo Zagorakis in, but Samaras and Stelios Giannakopoulous were off. Guus Hiddink reacted by bringing on Tony Popovic on for Scott Chipperfield early in the second half.
Substitute Panagiotis Lagos squandered Greece's best chances of the match twice in two minutes, shooting wide of Kalac's goal on both occasions. Georgios Seitaridis was then called in to clear a dangerous cross from Sterjovski in one of the few forays forward by the Socceroos in the opening period of the second half.
As the tempo of the game dropped around the hour mark, Skoko was replaced by Luke Wilkshire with Viduka given a rest, replaced by another local hero, Melbourne Victory's Archie Thompson.
The fatigue, which Hiddink had spoken of before the match, appeared to set in among the Socceroos after this, and Greece could have been level if Zagorakis had done better with his 70th minute effort, which he skied well over the crossbar from just inside the penalty area.
The ball was then moved quickly up the other end where Sterjovski could only put his header wide from a good position. Stan Lazaridis replaced him soon after.
A Zeljko Kalac fumble from a corner late in the game sent a flutter through Australian fans' hearts, with the Greek strikers lurking with intent, while Luke Wilkshire went close with shot from outside the penalty area.
Jason Culina, who looked very much at ease in his new midfield role, then produced a cracking shot which Nikopolidis spilt. It proved the final chance of the match.
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