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After an early try for Jonny May it was 13-13 at the break but Elliot Daly, Joe Cokanasiga and Owen Farrell underlined England's second-half dominance as a try in each half for Israel Folau flattered the tired-looking tourists.
The result followed wins for England over South Africa and Japan and a one-point defeat by New Zealand and has got them right back on track after a poor Six Nations and 2-1 series defeat in South Africa in June.
"It was a bit like Japan, we got seduced and thought it was going to come easy," said England coach Eddie Jones.
"We were confident we would get the job done in the second half."
Co-captain Farrell added: "We started well in the first half and then went away from it a bit. After the break we played direct and took it to them and things seemed to go our way after that.
"I think we always back ourselves here, there are brilliant players everywhere you look and hopefully our togetherness has shown. Hopefully that is only going to get better."
The result capped a dire year for Australia, who have now lost 11 of their last 15 matches and were second-best all day long at Twickenham.
Coach Michael Cheika was also furious that Farrell went unpunished for what he thought was a no-arms charge on Izack Rodda during a rare Australian attack.
Cheika said that he had been assured at the start of the tour that such tackles would be clamped down on and was outraged that the referee ruled that his lock had been the man dropping his shoulder.
"The idea that our player would have run into him was ludicrous," he said.
Cheika was clutching at straws, however, as his team, beaten by Wales two weeks ago, were outclased.
For the second week running England scored a try within three minutes as a powerful scrum set up May to cross in the right corner. Against Japan it all went wrong for the rest of the first half but England stayed on the offensive this time, albeit without making their domination count on the scoreboard.
Two Farrell penalties stretched the lead to 13-3 but the game had something of a Barbarians feel, with multiple turnovers and very little multi-phased attack – just the sort of situation where Australia’s backs thrive.
They were missing two of their best, however, after Adam Ashley-Cooper and Kurtley Beale were left out for disciplinary reasons.
Those who were playing had barely featured until winger Dane Haylett-Petty had a try ruled out for a forward pass after 27 minutes but the TMO became involved only after the Twickenham crowd roared their disapproval at the big-screen replay. There was no doubt about their next score though as fullback Folau burst through Ben Youngs’s tackle to cross under the posts after England had yet again kicked away possession.
England still looked on top but could not put any phases together and the Wallabies would have been delighted to reach the break level at 13-13 after Matt To’omua’s second penalty. England seemed to get the message at halftime that driving the ball through the forwards was the way to go and they duly did that, making space for Farrell to unload for Daly to score a superb try.
Cokanasiga then made it two tries in two matches after another chaotic passage of play and the 18-stone winger was then stopped inches short of a second after another bruising run a minute later.
Then it was England’s turn to have a try ruled out by the TMO, May’s 80-metre kick and chase ruled out for the ball clipping the touchline. The frustrated home fans soon had more to cheer though as Farrell sliced through the tiring Wallaby defence for England’s fourth try, and Folau’s last-gasp consolation did little to dampen the celebrations.
England have now won 24 to Australia’s 25 in the fixture and are next in action in the Six Nations in February away to Ireland.