Mathew Leckie scored a last-gasp winner as Australia claimed a 1-0 victory at the ANZ Stadium in the first of a double-header with Greece.
Ange Postecoglou's men, beaten 2-1 by England last time out, controlled a match that went ahead after a late pitch inspection following heavy rain in Sydney.
But they had to wait until the last kick of the game to win it, Leckie firing home after fellow substitute Tim Cahill's header had earlier been ruled out.
Though conditions were far from ideal, the Socceroos coped well and created numerous openings, most notably when Nathan Burns fluffed his lines after being sent through on goal in the first half.
Trent Sainsbury struck the woodwork in a second period that saw the introduction of Cahill, whose last-gasp header sparked wild celebrations that were cut short when it was ruled Alex Gersbach's corner had gone out of play.
Australia were not to be denied, though, and Gersbach laid on the assist for match-winner Leckie.
Greece, who missed out on qualification for the European Championship - a tournament they won in 2004 - saw goalkeeper Orestis Karnezis taken off injured to compound a disappointing evening.
Michael Skibbe's side will get a shot at revenge when the two teams meet again in Melbourne on Tuesday.
Apostolos Giannou, who represented Greece in a November friendly against Turkey, started up front for the hosts, who had much the better of a scoreless first half despite an early scare.
Iralkis striker Apostolos Vellios sent an early near-post header off target in a lively start that saw Karnezis clattered by Mile Jedinak at a corner.
Despite initially carrying on, Karnezis was replaced by Stefanos Kapino with just 15 minutes gone and was later taken to hospital with suspected broken ribs.
Burns wasted an excellent opportunity to break the deadlock midway through the opening half, scuffing his shot wide from inside the box after excellent build-up play from the Socceroos.
The hosts continued to grow into the contest and Mark Milligan fired another warning shot as he blasted narrowly over the crossbar from 20 yards.
Kapino was forced into a fine one-handed save as he back-pedalled to tip a sliced attempted clearance from Marios Oikonomou over the top in the 38th minute.
Australia saw strong shouts for a penalty waved away when Giannis Maniatis dived in on Robbie Kruse, while Kapino showed superb reflexes to keep out Milligan's strike on the stroke of half-time.
Jedinak cleared the crossbar with a free-kick early in the second half as Postecoglou's side continued to search for the opener.
Giannou may well have been relieved to see an offside flag raised when he somehow turned Jason Geria's 53rd-minute cross wide from six yards.
The home crowd were buoyed by the arrival of the influential Cahill for the final 18 minutes, but Vasilis Torosidis almost silenced them when he headed wide from close range.
A bursting run from Tom Rogic ended with a tame shot wide of goal and after Sainsbury struck the post late on, with Australia's frustration apparently compounded when Cahill's header was chalked off.
However, Leckie struck from the edge of the box to settle matters in dramatic fashion.