The 31-year old now scored a record 5443 runs for England in his 6187 ODI runs.
"I did know at the start of the series I was close and to pass someone like Ian Bell (as highest ever ODI scorer) is something that is satisfying and the way I struck it today you just have to do that", he said.
Australia captain Tim Paine maintains his beleaguered side can prevent a series whitewash against England despite their Trent Bridge traumas. Over the past four years, England team not only came over their embarrassing ODI World Cup performance but also managed to become an elite ODI team.
Brisbane Courier-Mail newspaper: "England has heaped further humiliation on an Australian one-day team in freefall..."
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Bairstow and Jason Roy had put on 159 for the first wicket when the opener was dismissed for 82 trying to take on the arm of D'Arcy Short before being run out by Paine. In Cardiff and Nottingham, their bowlers were dispatched for over 820 runs.
England have not played an ODI in Durham since 2015 but their recent record in the north-east is good having won five of their last six completed matches there.
AJ Tye went wicketless for 100 runs from nine overs with Jhye Richardson the pick of the bowlers with unflattering figures of 3-92.
There was no let-up in the astonishing run-rate, however, as Bairstow - who had two scares, overturning an lbw verdict against him on 27 and then escaping a very hard chance to Marcus Stoinis at deep mid-off three runs later - powered on to a 69-ball century.
Switzerland Boss Vladimir Petkovic 'Proud and Pleased' After Impressive Draw Against Brazil
The coach didn't want to criticise the referee after Gabriel Jesus went down in the Swiss area in the second half, but he did say he thought Zuber had pushed defender Joao Miranda prior to the equalizer.
England's Eoin Morgan bats during the third One-Day International (ODI) cricket match between England and Australia at Trent Bridge cricket ground in Nottingham, central England on June 19, 2018. It was his fourth ton in last six innings.
"The wicket was still terrific when we batted on it as well". Apart from the batsmen-friendly tracks, the fielding restrictions and heavier bats are just additions that suppress the bowlers even more. It was a remarkable day's cricket, but you wouldn't want every day to be like this. The top three are a huge asset to have.
Germany v Mexico, 17 June 2018
And when Rafael Marquez came on in the 74th minute he made history too, tying a record by playing in his fifth World Cup . Germany qualified for the tournament with a flawless record of 10 games played, 10 games won.