Having won the toss, visiting captain Tim Paine asked England to bat first on a beautiful batting wicket and Jason Roy and Bairstow were quickly on the attack.
The latter crunched three boundaries in only the second over and Roy was soon in on the act, too, taking Billy Stanlake for 14 in the fifth.
The pair had taken England to 79-0 after only ten overs and brought up the 100 soon after.
Both passed fifty before Roy was dismissed for 82, brilliantly run out by D'Arcy Short in the deep having come back for a second run, but Bairstow and Alex Hales went on to produce a brutal onslaught against a wilting Australian attack that is clearly missing Mitchell Starc and Pat Cummins.
Hales was quickly into his work, brushing aside any pressures he might be feeling about the impending return of Ben Stokes, and he brought up his half-century in 38 balls before going on to reach three figures from only 62 deliveries.
In between those milestones, Bairstow continued his stellar run of form with a magnificent innings of 139 which was eventually brought to an end by Ashton Agar whose figures of 10-0-70-1 were quite respectable in the circumstances.
The boundaries, nor the records, didn't end there, however, with Eoin Morgan making a rapid 21-ball fifty before England stuttered slightly in the closing overs as Jye Richardson picked up three wickets for the tourists.
In reply, Australia were never really in the hunt despite promising contributions from Travid Head (51) and Marcus Stoinis (44).
Head began brightly, taking a liking to David Willey, but just as he seemed set to make a big score, he offered a simple return catch to Moeen Ali who went on to claim three wickets.
Stoinis was another who looked to have his game in good order but he was caught short when taking on Bairstow's arm in the deep and cut a frustrated figure as he left the field with Australia's chance all but gone with his dismissal.
While Ali found good drift and spin with his off-breaks, Adil Rashid also extracted some turn from a true pitch and the Yorkshire leg-spinner had too many tricks for the Australian lower order as he finished with figures of 4-47.
England captain Morgan hailed a "complete performance" after the game.
"It's a day for everyone in the changing room to be very proud of," Morgan said.
"How we operated and the level of intensity was on a different level to any ODI in the past three years.
"It was close to a complete performance and we saw some outstanding performances."
Australia captain Tim Paine paid credit to England's performance.
"That was extraordinary. Some of the best striking I've seen to be honest," he said.
"The English boys are very hot - they put us to the sword.
"That is as hard a day's cricket as I have had in 16 or 17 years. We have had some young guys in our changing room experience it really early in their career.
"We are trying to learn, and learn really quickly, so today was certainly a learning experience."
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