The Wallabies have qualified for the World Cup quarter-finals and eliminated one of their main rivals for the title with a dramatic 33-13 win over England at Twickenham.

SCOREBOARD: ENGLAND 13-33 AUSTRALIA 13-33 at Twickenham, October 4 2015 49% Possession 51% 47% Territory 53% 86 Tackles 98 10 Offloads 9 England: A Watson try, O Farrell 2 pens, 1 con Australia: B Foley 2, M Giteau tries, B Foley 4 pens, 3 cons

The victory on Sunday morning (AEST) - their biggest ever at Twickenham - lifts Australia to the top of Pool A, ahead of Wales on points difference, and consigns England to the ignominy of being the first World Cup hosts to fail to reach the knock-out stages.

Bernard Foley stole the spotlight with a flawless two-try display and 100 per cent kicking record as he enjoyed a personal haul of 28 points to silence the 81,010-strong crowd.

The win is Australia's first over England at a World Cup since the 1991 final at Twickenham, and goes some way towards avenging quarter-final losses in 1995 and 2007 - not to mention the 2003 final.

The Wallabies had to withstand a second-half comeback, as England drew within seven points with 15 minutes remaining.

But that was snuffed out with the 71st minute sin-binning of England five-eighth Owen Farrell for tackling Matt Giteau without the ball - with Australia kicking two more penalties before running in an 80th-minute try to veteran Matt Giteau to complete the rout.

Australian set piece holds firm

Sorry, this video has expired Wallabies knock host England out of the World Cup

It gave Foley an Australian points record against England, bettering that of Matt Burke's haul in the 76-0 thrashing in 1998.

The unfashionable number 10 who has had to fight the polarising Quade Cooper to hold onto his spot in the team, crossed for a brace of first-half tries and knocked over both conversions and a penalty as the Wallabies led 17-3.

Makeshift number eight David Pocock was again outstanding at the breakdown, as England had no answer to the brilliant ball thief, coughing up possession time and again.

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Much of the pre-match talk centred around the scrum, and whether the Wallabies would turn to mush as they had in the past.

Instead the opposite happened and England fell to pieces, conceding three first-half scrum penalties - and six by full-time - as respected French referee Romain Poite came down hard on English loosehead prop Joe Marler for boring in at an angle.

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Marler was hooked after 50 minutes following a terse exchange with Poite about coming in at an angle after he had conceded a fourth penalty.

With England's set piece failing to fire, the Wallabies' electric backline was given time and opportunity to unleash - and they did.

An early chance was squandered when star full-back Israel Folau butchered an overlap, with winger Rob Horne open outside him.

But Foley ripped the game wide open when he crossed twice in a five-minute period.

For the first, he found a gap between England's Ben Youngs and Joe Launchbury before breaking through the defence of fullback Mike Brown to score.

Five minutes later, the Wallabies targeted the same two defenders with a clever set play - Foley turning the ball inside to Kurtley Beale who split the defence, drew the full-back and found Foley in support for his second.

Beale was forced into the fray early, coming off the bench after 11 minutes to join the wing following a shoulder injury to winger Rob Horne.

AAP