England regained the Cook Cup with a dominant pack display as Australia slumped to their seventh straight loss.
Despite going 6-3 behind after two Mat Rogers penalties, England went ahead after a well-worked try from Ben Cohen.
Charlie Hodgson added a drop goal and a penalty to make the score 16-9 but Australia battled their way back into the game with a try from Drew Mitchell.
England dominated possession and finally sealed the win when wing Mark Cueto crossed five minutes from time.
The victory is a real boost for an England side that have struggled for form and results in the two years since winning the World Cup.
Although at times England looked laboured in attack as they spurned a host of chances, Andy Robinson's men ground Australia down up front to set the platform for victory.
Australia, who have now equalled their worst run of results since 1969, showed some impressive signs going forward but the scrum disintegrated under pressure.
After a nervy start from England, Australia got the first points when scrum-half Matt Dawson lost control of the ball while he was preparing to clear from the base of a ruck and Rogers kicked over.
The Wallabies did not look like a team that were struggling for form and they should have added to their total when flanker George Smith released wing Mitchell but Sale fly-half Hodgson saved the day with a last-ditch tackle.
England were struggling to get their rhythm but Hodgson kicked over on 14 minutes when skipper George Gregan blocked Josh Lewsey as he tried to chase his own kick.
Mark Cueto has a fine try-scoring record for England
Australia almost scored again soon after when full-back Chris Latham made a darting break only for Hodgson to bring him down near the line.
England flanker Lewis Moody was sin-binned trying to stop the attack as Australia scented a try and Rogers added his second penalty.
The game seemed to turn on 27 minutes when Gregan was yellow carded and a minute later Lewsey's long pass found Cohen in plenty of space and the Northampton man crossed to mark his return to the international stage.
With 14-man Australia being pummelled by England's pack, the home side should have added to their tally before the break.
They did straight after half-time when Hodgson coolly slotted over a drop goal to make the score 13-6 after an aggressive start to the second period.
Rogers added his third penalty soon after but England again spurned another glorious chance near the Australia line when Corry was penalised for crossing.
Hodgson slotted over again but Australia showed their character when Mitchell powered over after an earlier break from Latham and Rogers' conversion levelled the match at 16-16.
Worryingly for England, Hodgson limped off to be replaced by Olly Barkley and the Bath man soon made his presence felt with a superb long-range penalty from just inside his own half.
England's dominance in the scrum was highlighted as the game entered the final 11 minutes and prop Al Baxter was sin-binned as another set-piece collapsed underneath the Australian posts.
The game was then reduced to uncontested scrums when Aussie prop Matt Dunning was stretchered off.
England kept the pressure on and sealed the win when Cueto burst through the line to make his record nine tries from nine caps.
Despite the win, focus must now switch to the task of New Zealand next week, who will provide a much sterner test than this weakened Australia side.
England: Lewsey; Cueto, Noon, Tindall, Cohen; Hodgson, Dawson; Sheridan, Thompson, Vickery; Borthwick, Grewcock; Sanderson, Moody, Corry (capt).
Replacements: Barkley for Hodgson (57).
Not used: Mears, Stevens, Deacon, Jones, Ellis, van Gisbergen.
Sin bin: Moody (16).
Australia: Latham; Gerrard, Tuqiri, Turinui, Mitchell; Rogers, Gregan (capt); Dunning, Cannon, Baxter; McMeniman, Sharpe; Roe, Moore, Smith.
Replacements: Giteau for Gerrard (70), Johansson for Turinui (73), Polota-Nau for Dunning (70), Chisholm for McMeniman (70), Fava for Smith (77).
Not Used: Holmes, Whitaker.
Sin Bin: Gregan (27), Baxter (69).
Referee: Joel Jutge (France).