Aaron Finch (76) and Shane Watson (82) were in the runs this time as the host ran down a revised total of 275 off 48 overs after rain interrupted play.
It took James Faulkner to finish the job in the final over to clinch a 4-1 series win over the previous world leaders.
The victory also provided some good news for fans after a diabolical tour in the Middle East against Pakistan.
Watson’s knock probably locks in his spot in the Test side to take on India, even if it was in the shorter format.
This was the 33-year-old crock’s first ODI half-century for more than 12 months and it was against the world’s best attack.
Pat Cummins took three wickets for himself and gave the selectors a nudge that after his own injury woes he could well be a handy firebrand when the World Cup comes around.
While others struggled, he sent not just Hashim Amla to the pavilion but the world’s best batsman AB de Villiers for 91.