Jonny Wilkinson scored all of England's points
Australia (10) 10
England (6) 12
Pens: Wilkinson (4)
Jonny Wilkinson was the scourge of Australia again as his four penalties put England in the World Cup semi-final after a thrilling win in Marseille.
Lote Tuqiri's try put Australia 10-6 up but Wilkinson's boot and a dominant scrum kept England in the game.
There was little flowing rugby in the second half but England's powerful pack gradually ground Australia down.
Stirling Mortlock and Wilkinson both missed late kicks, but England held on and will now face France in the semis.
Wilkinson may well claim the headlines with his 12-point haul - which made him the World Cup's all-time leading point-scorer - but it was England's pack which did the real damage to an Australia side who were odds-on to make the last four.
England's front row of Andrew Sheridan, Mark Regan and Phil Vickery pulverised Australia at the scrum and laid the platform for the back-row trio of Lewis Moody, Martin Corry and Nick Easter to nullify George Smith at the breakdown.
Despite Mortlock's penalty giving Australia an early lead, he missed two other kickable chances as England had the better of the opening 40 minutes.
An unlucky bounce from Mike Catt's kick into the right-hand corner denied Paul Sackey the chance to score for England's opening try.
England were totally on top at the scrum, but the early penalties at the set-piece went against them as Australia tried to neutralise their opponents' advantage.
A trademark Jason Robinson burst of speed tore through the defensive line as the defending champions finally found the fluency in attack which has eluded them for virtually the entire tournament.
Andrew Sheridan had Australia's front row on the back foot for the whole match
Mathew Tait was central to England's next burst forward, involved several times in a sweeping cross-field move but for all their pressure, the only change to the scoreline was two Wilkinson penalties.
The Wallabies made England pay when Tuqiri eluded the grasp of Josh Lewsey to stretch over in the right-hand corner, finishing off after Berrick Barnes' clever dummy allowed Mortlock's battering-ram run to set up the try.
The score, improved by Mortlock's superb conversion, put Australia four points up at the break but soon after the restart it looked like England's pack had set up their first try.
The pack was in reverse as George Gregan was smothered by Lewis Moody and Andy Gomarsall, trying to get the ball away.
But with the try-line within reach, Wilkinson's pass caught Catt unawares and he knocked on.
Although the attack failed to produce a try, Wilkinson notched another penalty to reduce the deficit to 10-9 as a rattled Australia started to lose their discipline.
Australia were attempting to re-establish themselves in the game when Tait's inspired hack from a stray pass by George Gregan sent play back down the other end of the field.
Rocky Elsom was panicked into conceding a penalty that Wilkinson slotted over to give England the lead.
Australia did engineer a massive overlap on halfway, but Sackey took a gamble by coming in off his wing to take Mortlock man-and-ball, and the decision proved a try-saver as the Aussie captain lost possession.
Drew Mitchell's introduction instantly gave Australia more punch in attack but Nathan Sharpe's knock-on at the vital moment scuppered a dangerous attack.
When Gregan - who was out-of-sorts throughout - conceded a clear penalty for offside on the halfway line, it seemed set up for Wilkinson to apply the finishing touch to another memorable win, but his kick drifted inches wide of the left-hand post.
Mortlock then had a chance to snatch a late victory for Australia with a penalty, but made a mess of it and England held on for their biggest result since the 2003 World Cup final.
England: Robinson; Sackey, Tait, Catt, Lewsey; Wilkinson, Gomarsall; Sheridan, Regan, Vickery (capt), Shaw, Kay, Corry, Moody, Easter.
Replacements: Chuter, Stevens, Dallaglio, Worsley, Richards, Flood, Hipkiss.
Australia: Latham; Ashley-Cooper, Mortlock, Giteau, Tuqiri; Barnes, Gregan; Dunning, Moore, Shepherdson, Sharpe, Vickerman, Elsom, Smith, Palu.
Replacements: Freier, Baxter, McMeniman, Hoiles, Waugh, Huxley, Mitchell.