Morgan took just 21 balls to reach his half-century, the fastest by any England batsman in terms of balls faced.
England stormed to a one-day worldwide world record of 481 for six as they thrashed Australia by 242 runs at Trent Bridge to take an unassailable 3-0 lead in the five-match series on Tuesday. When Alex Hales (147) hoisted Jhye Richardson for six in the 46th over, it meant England had broken its own world record total - also set at this venue - of 444 for three against Pakistan in 2016.
Meanwhile, Eoin Morgan became England's top-run scorer in ODI cricket (5443 runs), who went past Ian Bell's tally of 5416 runs.
After his bowlers were smashed for a record-breaking total of 481 for 6 from 50 overs, Paine then saw his batting line-up bowled out for 239 to hand England an unassailable 3-0 series lead.
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By contrast, this was England's biggest victory in the format, topping their 210-run win against New Zealand at Edgbaston in 2015.
Jason Roy, who made 120 in England's 38-run win in the second ODI in Cardiff on Sunday, could have had back-to-back hundreds but instead ran himself out on 82.
Bairstow had two scares, overturning an lbw verdict on 27 sweeping at Ashton Agar and escaping a very hard chance to Marcus Stoinis at deep mid-off three runs later off Andrew Tye, but he powered on to a 69-ball century.
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Having had the stuffing knocked out of them by England's batsmen, the Aussies were then humbled by the bowlers, with Travis Head the only tourist to pass 50.
Alex Hales eclipsed Bairstow with a sublime 147, a total that included 16 fours and five sixes. The match run-rate of 8.27 is also the 2nd highest in an ODI game behind 8.73 in the 2006 Johannesburg ODI between South Africa and Australia. In a series of social media posts, Ganguly wrote, "To see nearly 500 runs scored in 50 overs in England is scaring me, bout the health of the game and where it's going". Overall, England thrashed 41 fours and 21 sixes.
The previous mark was 59, held by England, against Lanka.
Sourav Ganguly, former Indian captain, has expressed his concern over the health of the game cricket after England posted an ODI record total of 481/6 against Australia on Tuesday.
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