Eoin Morgan (67) put in a supporting bid for the headlines by hitting England's fastest ever 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.
With Tuesday's victory, England have now taken an unassailable 3-0 lead in the ongoing 5-match ODI series. During the run-chase, Australia huffed and puffed and were never in contention to trace down the mammoth score. Surrey had hammered the gargantuan total against Gloucestershire at The Oval during the 2007 Friends Provident Trophy.
Bairstow smashed his fourth ODI century in 2018 and Hales took England past their old record with a six, the 21st of the innings.
In the intervening years, they have developed into the most exciting, destructive and successful one-day team in the world.
England have broken the record for the highest score in ODI cricket with a brutal display of hitting against Australia, winning by 242 runs.
In response, Australia fell well short of the record target, making 239 all out in 37 overs.
Left-arm spinner Ashton Agar thought he had Bairstow lbw for 27 when he missed a sweep but the batsman's review showed the ball, surprisingly, missing leg stump.
The defeat was Australia's worst in 915 ODIs stemming back to 1971 and usurping the 206-run loss to New Zealand 32 years ago.
In the process, he surpassed former England cricketer Ian Bell's 5416 ODI runs.
Buttler followed shortly after, having been sent in up the order at four, before Hales and Morgan added 124 runs in just 59 balls. The visitors will need to reverse history as only twice have teams breached the 400-run mark whilst batting second in ODIs.
Moeen, who was dropped from the Test team after a hugely hard winter in Australia and New Zealand, has taken eight wickets in the first three games of the series, including three today. Suffice to say, all pretence of maintaining a balance between bat and ball disappears in such circumstances. The top three are a huge asset to have.
They managed to win 2010 T20 World Cup but failed to impress much in 50 over World Cups.
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