Set 160 to win on the final day in Sydney, Australia looked in control at 2-92 shortly after lunch.
But a mini collapse of 3-29, headlined by Marnus Labuschagne being run out for 37, briefly left Australia with a tricky fourth-innings chase.
Alex Carey (16no) and Cameron Green (22no) were then able to get the side home, ensuring England would not reduce the series margin to 3-2.
On a chaotic final day, Usman Khawaja missed the chance to sign off by hitting the winning runs in his last Test when bowled by Brydon Carse for six.
Ultimately though, a crucial 62-run opening-partnership stand between Travis Head (29) and Jake Weatherald (34) proved vital, with England flat early in the field.
The tourists had began the day at 8-309 with a 119-run lead, needing Jacob Bethell to carry them to a competitive score.
And while he was eventually caught behind off Mitchell Starc for 154, the 22-year-old's maiden first-class century will offer hope to England for the future.
More immediately though, a period of heavy introspection looms over the team, its culture and Brendon McCullum's future as coach after a tour of wasted opportunities.
Australia's 4-1 series victory this summer will go down as one of their most impressive, considering who they have done it without.
Pat Cummins played just one Test, Josh Hazlewood was sidelined for the whole summer and Nathan Lyon bowled two overs in Perth before being hurt in Adelaide.
Khawaja and Steve Smith both missed a Test through injury, with limited chances meaning the latter was only dismissed five times in the series.
Yet Australia still cantered to victory with relative ease in most Tests, winning every big moment with the exception of their second-innings collapse in Melbourne.
Head's 69-ball century in Perth, when moved up to open for an injured Khawaja, set the tone for the summer, with more tons at the top following in Perth and Sydney.
And with the rest of Australia's first-choice attack missing, Starc was superb with 31 wickets at 19.93 for the series.
Beyond him Michael Neser and Scott Boland have both stood up, with Neser in particular an unlikely hero after being left out of the initial squad.
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