World Cup 2010 - Australia and Serbia tumble out
That came back to haunt the European side in the second period as Australia took control.
Tim Cahill gave them the lead with a glorious header from 12 yards on 69 minutes before substitute Brett Holman, on for Mark Bresciano on 66 minutes, smashed a shot into the corner of the net from 25 yards.
Serbian substitute Marko Pantelic pulled one back for Serbia from close range on 84 minutes and despite some frantic late attacks which saw the Serbians have an effort disallowed for offside, a penalty claim waved away by Uruguayan Jorge Larrionda and Pantelic miss a gilt-edged chance, Australia held on for a win that will at least give them some comfort on the flight home.
Serbia and Australia had never met before this encounter, but it will be Serbia who will probably feel sorer when they reflect upon this campaign.
They beat Germany 1-0 and had plenty of opportunities to carve out a lead against Pim Verbeek's side.
Serbia enjoyed enough possession to wreak havoc, but noticeably lacked a cutting edge.
Krasic saw an effort beaten away by Schwarzer on five minutes. He should have given his side the lead they craved seven minutes later.
The striker dashed clear of the Australian defence and was past Fulham keeper Schwarzer, but rushed his shot and blazed over from an angle that was hardly acute.
Schwarzer was called into action on 22 minutes as Branislav Ivanovic darted into the Australian box, but the keeper made a breathtaking, solid one-handed stop.
Nikola Zigic then blew a glaring opportunity as he sent a free header past the post.
Australia's best contribution of the first half was a Cahill header, but the Everton player would soon show off his celebrated ability in the air.
There appeared little danger as a ball arrived in the heart of the Serbian area, but Cahill rose higher than Nemanja Vidic to plant Brett Emerton's cross into the corner of the net from the penalty spot.
The Australian fans were in a party mood and they welcomed in a second minutes later when Holman, who scored against Ghana in a 1-1 draw, scampered clear to send a shot low spinning past the diving Serbian keeper Vladimir Stojkovic from 25 yards.
A lovely dipping shot from distance by Zoran Tosic was spilled by Schwarzer and Pantelic followed in to score on 84 minutes to breathe new life into the group.
Serbia were suddenly back in the hunt. Pantelic had a goal marginally ruled out for offside and Cahill appeared to handle the ball in the box before an unmarked Pantelic sent what should have been an easy tap-in over the bar.
Larrionda was surrounded by angry Serbian players and coach Radomir Antic after he blew the final whistle as they missed out on the second round.
Australia v Serbia
1st Half Goals 0-0
Shots on Target 7-6
Shots off Target 6-12
Blocked Shots 6-4
Yellow Cards 3-2
Red Cards 0-0
Passing Success 78.4%-88.7%
Tackles Success 72.2%-60%
Territorial Advantage 45.1%-54.9%