A series of costly second-half errors and a controversial video replay decision combined to see Australia fall two tries to one.
England scored both their tries midway through the second half and the Wallabies failed to cope with the pressure in front of a capacity 80,000-strong crowd.
Ewen McKenzie's men will be kicking themselves for giving away a great opportunity as they were looking good at 13-6 up early in the second half.
The match turned after vice-captain Quade Cooper missed a penalty attempt and then England man-of-the-match Mike Brown plucked a Matt Toomua touch-finder out of the sky and counter-attacked off his line.
Video replays showed fullback Brown standing on the sideline at the time but it counted for nought once England captain Chris Robshaw scored at the other end from a charged-down Will Genia box-kick.
Scott Fardy was stretchered off with a suspected neck injury amid all the mayhem.
The dust wasn't allowed to settle as playmaker Owen Farrell then strolled over as he ghosted between Stephen Moore and Ben Mowen.
Moore had been blocked by an off-side English attacker but television match official Marshall Kilgore adjudged "there wasn't enough of an obstruction" to deny the try after it was referred upstairs.
Cooper, who kicked three from three in the first half, missed another penalty attempt to draw closer but they were ultimately overpowered at the contact zone at critical times.
The Wallabies play Italy in Turin next Saturday and their ensuing games against Ireland, Scotland and Wales no longer hold the same interest with hopes of a second-ever grand slam shot.
The English started better and counted themselves unfortunate not have a wider lead than 6-3 after the first half hour as their scrum dominated but Farrell uncharacteristically missed three straight kickable penalties.
With one of their few attacking forays before the break, the Wallabies hit back when Cooper found Israel Folau, impressive again, with a beautiful cut-out pass from a solid scrum.
Folau shrugged off Chris Ashton and then from the ensuing plays centre Toomua bowled over opposite number Billy Twelvetrees from close range to cross.
It was the sort of ruthless finishing precision which Australia has sorely lacked in their first 10 Tests of the year.
A slippery pitch made it hard for defenders to get their footing and no one exploited it better than Brown who was dangerous whenever he touched the ball.
Genia had a game to forget with his boot and was replaced midway through the second half by Nic White.