The nervy hosts lost five wickets as they chased their 160 target, which they reached after lunch on day five with Cameron Green not out 22 and Alex Carey on 16.
Australia lost openers Travis Head (29) and Jake Weatherald (34), along with captain Steve Smith (12) and Khawaja who made six in his final knock before retiring after an 88-Test career.
Marnus Labuschagne, dropped on 20, compiled 37 before needlessly running himself out to give Ben Stokes’s men a flicker of hope as they reduced Australia to 121-5.
But victory was never seriously in doubt after England were dismissed for 342 on the back of Jacob Bethell’s stylish 154.
Defeat culminated a long tour for the visitors that quickly turned into a horror show when they lost the opening two Tests in Perth and Brisbane by eight wickets and the third at Adelaide by 82 runs.
Stokes’s side had arrived confident they could win their first series in Australia since 2010-11 amid taunts about the hosts having their worst side in 15 years.
Facing heavy criticism over their preparations, discipline and ultra-aggressive “Bazball” style of cricket, they rallied to pull off a stunning four-wicket comeback win in the fourth Test in Melbourne.
It was their first victory in 18 Tests on Australian soil and restored some pride, but another loss in Sydney, albeit close, will see them face a tough inquisition on their return home with coach Brendon McCullum’s job on the line.
Australia achieved their success despite being without pace spearhead Josh Hazlewood for the series and Pat Cummins for all but one Test, while veteran spin king Nathan Lyon played a limited role.
Nearly 860,000 fans watched the series with a record 211,032 through the turnstiles in Sydney. (AFP)
