The hosts wrapped up an unassailable 3-0 series lead with a mammoth 242-run win – their biggest in one-day internationals, and Australia’s heaviest defeat –after surging past their own previous global all-time high of 444-3 at this same venue two years ago.
Eoin Morgan (67) put in a supporting bid for the headlines by hitting England’s fastest 50, from 21 balls in the third century stand of the innings, before he and Hales (147) holed out to successive balls from Jhye Richardson.
Australia, who had put England in on a pitch that made bowling a wildly unenviable task for all, then unsurprisingly could not sustain a plausible chase as Moeen Ali (3-28) and Adil Rashid (4-47) put the brakes on in a reply that crumbled to 239 all out in 37 overs.
Bairstow (139) and Jason Roy (82) were England’s first two driving forces in an opening stand of 159 that was broken only when the latter was run out by an excellent throw from D’Arcy Short in the leg-side deep with Roy trying to steal a tight second run in the 20th over.
There was no let-up in the unprecedented run-rate, however.
Bairstow had two scares, overturning an lbw verdict on 27 sweeping at Ashton Agar and escaping a very difficult chance to Marcus Stoinis at deep mid-off three runs later off Andrew Tye, but he powered on to a 69-ball century.
It was his fourth in his last six ODI innings and although he was eventually caught pulling Agar to deep midwicket, having hit 15 fours and five sixes, No 3 Hales dovetailed and then took over to the delight of his home crowd.
The pair put on 151, and Hales, whose hundred came from just 62 balls, finished like Bairstow with five of England’s 21 sixes.
Morgan hit six of them and, for good measure, went past Ian Bell as England’s all-time record ODI runscorer.
The captain was cashing in expertly on the brilliance of those above him in the hosts’ powerhouse top order.
England’s openers set a remarkable tempo, and Australia had no answer as Tim Paine deployed eight different bowlers in the first 24 overs – to no avail.
In the final analysis, Tye suffered most as his famed variations fell flat on a perfect surface and he was dispatched for 100 runs in nine overs, while Richardson’s changes of pace deservedly brought him three wickets, albeit at the cost of 92 runs.
Moeen was among those who got little or no chance to join in the fun as batsmen.
But he soon had a say with the ball, first tumbling low at mid-on to collect Short’s chip off David Willey to mid-on and then seeing off Travis Head caught-and-bowled just after the opener had reached a 36-ball 50.
The off-spinner was proving difficult to get after, and so it was again when Australia’s Cardiff centurion Shaun Marsh failed to get enough on an attempted straight six and was caught on the long-on boundary by Liam Plunkett – the second of two wickets for the addition of five runs leaving the tourists 100-3.
Only details remained and they all favoured world No 1 side England who can therefore contemplate the possibility of a first 5-0 ODI whitewash of their Ashes rivals.
Bairstow admitted he did not know where his current rich vein of run-scoring form is coming from.
“I’ve got no idea,” said the Yorkshireman. “It’s a case of following and watching the ball. Each opposition gives you different challenges. That’s the nature of players round the world. It’s a case of maintaining your consistency and doing the same things day after day and that’s what I’m finding at the minute.”
Man-of-the-match Hales said: “It’s as good as it gets. What a special day.
“We’re in a really good head space as a team. The pool of talent we have in England is as good as it’s been in white-ball cricket.”
Australia captain Paine, took his hat off to England’s performance, saying the hosts had been “red hot”.
“That was extraordinary. Some of the best striking I’ve seen to be honest,” he said.