TIM Cahill and Brett Holman scored magnificent goals to drive Australia to a 2-1 win against Serbia - but the Socceroos have been eliminated from the World Cup on goal difference.

Needing a victory and the result of the clash between Germany and Ghana in Johannesburg to go their way, the Socceroos kept up their end of the bargain with an inspiring effort highlighted by stunning goals from Cahill and Holman in front of 37,836 fans at Nelspruit.

But Germany's 1-0 win over Ghana wasn't enough for the Australians to reach the second round, with the Germans topping the Group D and the Ghanaians pipping the Socceroos for second spot on goal difference after both sides finished on four points.

Germany will now meet England in a tantalising round of 16 affair, with Ghana to meet Group C winners USA.

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Cahill and Holman gave Australia hope with goals within the space of four frenetic second-half minutes.

But an error from Socceroos goalkeeper Mark Schwarzer that gifted Serbian substitute Marko Pantelic a tap-in goal in the 84th-minute ended any hope of Australia pulling off a miracle by qualifying for the second round.

The Socceroos' hefty 4-0 loss to Germany in Durban proved Australia's downfall, with the goal difference too much to peg back.

Coach Pim Verbeek hailed the "great result" after the game, saying he was delighted with the spirit of his men.

"We have four points, I was hoping it was enough, but after all the goal difference against Germany killed us," Verbeek said.

In the opening moments of the match, Serbia's CSKA Moscow star Milos Krasic made himself an instant enemy of the pro-Socceroos crowd when he appealed for a penalty after a harmless bump from Australian midfielder Carl Valeri.

Despite Krasic's protests, referee Jorge Larrionda waved play on, with the Serbian attacker then constantly jeered every time he touched the ball.

But it didn't stop him demanding possession, with Krasic tormenting Socceroos left fullback David Carney, who was lucky to hold his place in the side ahead of the experienced Scott Chipperfield.

Krasic forced Socceroos keeper Schwarzer into a sharp save in the sixth minute, and was again in the action six minutes later after leaving Carney in his wake in running on to a sublime through ball from Milos Ninkovic.

But Schwarzer cleverly forced Krasic out wide enough for the Serbian's shot to miss the target.

The Serbians continued to dominate, with Schwarzer required to pull out his very best to deny defender Branislav Ivanovic from point-blank range in the 22nd minute after some poor Australian marking in the penalty area.

Australia's first real chance of the contest came in the 32nd minute after a smart build-up involving Brett Emerton and Mark Bresciano.

It was Bresciano who delivered the final ball, a dangerous back post cross that Cahill met with interest. But the Everton star's header sailed wide.

Serbia hit back immediately, but wasted a golden chance to take the lead in the 34th minute.

Given far too much space on the ball by the struggling Carney, Zdravko Kuzmanovic floated a dangerous cross in between Socceroos central defenders Beauchamp and Lucas Neill.

The ball found an unmarked Nikola Zigic, but with only Schwarzer to beat, the 202cm giant failed to hit the target with his header.

Nine minutes later Bresciano found himself totally unmarked on the left and demanding the ball from Kennedy.

But the lanky striker dawdled on the ball, with the danger snuffed out by a grateful Serbian defence.

Kennedy had the chance to make amends in the final minute of the first half, but his header from an Emerton cross was a weak effort that went straight to goalkeeper Vladimir Stojkovic.

Cahill was in the thick of the action in the first minute of the second half, winning a free kick and remonstrating with the man who made the foul, Serbia's Manchester United star Nemanja Vidic.

Bresciano stood over the dead ball and whipped it low and hard into the penalty area but it was cleared away to safety.

Tensions continued to rise, with Socceroos pair Beauchamp and Luke Wilkshire booked within the space of three minutes for cheap fouls.

Zigic blew another opportunity to put the Serbians ahead in the 53rd minute after being found unmarked in the box by Milan Jovanovic. But the big man blazed his shot over the crossbar.

The challenges continued to fly in, with Ninkovic booked for a dangerous foul on Wilkshire in the 58th minute.

Bresciano's subsequent free-kick was tipped around the post by an alert Stojkovic.

The Serbian keeper was again called into action by Bresciano six minutes later, parrying a fierce 20m drive away to safety.

But the Socceroos were rewarded for their persistence when Cahill outjumped Vidic to head home a Wilkshire cross in the 69th minute.

Australia doubled their advantage four minutes later through substitute Holman. Running into space through the midfield, Holman unleashed a potent 25-metre strike that rifled into the corner of the net.

The Aussies' fighting spirit was all the more impressive considering that official World Cup statistics indicated Serbia had a massive man-for-man advantage over the Socceroos.

The Castrol Index - which analyses every pass, tackle and shot a player makes on the field - showed Serbia had no fewer than seven players ranked higher than Australia's number one - goalkeeper Mark Schwarzer, who at 7.07 ranks 196th in the tournament.

Winger Milos Krasic was the highest-ranked Serbian, with 8.06 squeaking him into the top 100 at 99th. Mindfielder Branislav Ivanovic is ranked 101st with a figure of 8.04.

Originally published as Superb Socceroos cruelly eliminated