England overcame both a dangerous Australia and their own shortcomings to grab a precious southern hemisphere scalp and get their autumn campaign off to a winning start.
Opportunistic second-half tries from skipper Chris Robshaw and fly-half Owen Farrell saw them overturn a seven-point deficit after Matt Toomua's try had seen them in trouble at the break.
Farrell kicked two penalties and added both conversions after earlier missing three kicks as the home side's superior scrum and forward power in the loose made up for a disjointed display elsewhere.
The win means England remain third in the International Rugby Board world rankings, with Australia - who could have displaced them with victory - staying in fourth.
More importantly, a decade on from England's sole World Cup win, it gives Stuart Lancaster's side precious momentum as they look to build towards the 2015 tournament that they will host.
The new centre combination of Joel Tomkins and Billy Twelvetrees had helped give England an early lead when they scragged Tevita Kuridrani to set up a penalty for Farrell, Quade Cooper levelling it up after Dan Cole went offside in a brisk opening period.
Farrell would miss three more from similar range as his forwards made impressive inroads at the scrum and in the loose, but after a barrelling run from Billy Vunipola on his full debut the Saracens fly-half made it 6-3 just before the half-hour.
England were dominating possession and territory without ever looking fluent, their reshaped back line showing its inexperience and lack of familiarity.
And when Israel Folau beat Chris Ashton on the outside after a fine pass from Cooper, Australia recycled close in to send centre Toomua across the line through Twelvetrees' lacklustre tackle.
With Cooper adding both the conversion and a quick penalty, the Wallabies had 10 unanswered points to silence a previously bellicose Twickenham.
Only a poor miss from the tee from Cooper kept the deficit at seven points as England's struggles worsened after the break.
It took a brilliant side-stepping run from full-back Mike Brown from his own corner flag - replays subsequently showed he was actually just in touch when he first gathered the ball - to spark both his side and the capacity crowd into life.
Only a desperate covering tackle from Adam Ashley-Cooper kept Marland Yarde out down the left after a quick tap penalty on halfway had been moved swiftly wide.
From the subsequent line-out Will Genia's clearing kick was charged down by Mako Vunipola, and Robshaw was quickest to the loose ball to gather and slide across the line.
Farrell's conversion levelled it up at 13-13 with half an hour left as Lancaster looked to add to the momentum by bringing on Ben Youngs, Dylan Hartley and Joe Marler.
It worked. Quick line-out ball was taken on by number eight Vunipola and then spread left to the dashing Brown, and although the Wallabies forwards slowed up the ball, Farrell spotted a gap between Stephen Moore and Ben Mowen to canter under the posts.
If there was a hint of obstruction from Hartley on Moore, then television match official Marshall Kilgore was happy to let it pass, allowing Farrell to make it 20-13 with the conversion.
Cooper had the chance to seize back the impetus in this topsy-turvy affair with a penalty from distance only to pull it wide, but with the lead a mere converted try nerves tightened as the seconds ticked away.
Handling errors continued on both sides, but England's superior forward muscle allowed them to squeeze the remaining life from the Wallabies and secure their fifth consecutive win at Twickenham.
For the visitors it was a further chastening reverse in a year that has seen them win only three Tests.
But England will go into next week's match against Argentina confident of extending their run before the visit of the All Blacks in a fortnight provides a far sterner test of their World Cup credentials.
England: Brown; Ashton, Tomkins, Twelvetrees, Yarde; Farrell, Dickson; M Vunipola, T Youngs, Cole, Launchbury, Lawes, Wood, Robshaw, B Vunipola.
Replacements: Hartley for T Youngs (54), Marler for M Vunipola (54), B Youngs for Dickson (54), Wilson for Cole (66), Morgan for B Vunipola (66), Flood for Twelvetrees (66), Attwood for Launchbury (75).
Not Used: Foden.
Australia: Folau; Ashley-Cooper, Kuridrani, Toomua, Cummins; Cooper, Genia; Slipper, Moore, Alexander, Timani, Horwill, Fardy, Hooper, Mowen.
Replacements: McCalman for Fardy (49), Kepu for Alexander (49), Foley for Ashley-Cooper (49), Robinson for Slipper (61), Douglas for Timani (62), White for Genia (66), Faingaa for Moore (68),
Not Used: Lealiifano.
Ref: George Clancy (Ireland).