The six-run win saw Scotland get one over their arch-rivals in style.
It was a brilliant performance by the Scots against an England team who are now top of the one-day global rankings.
Ex-New Zealand spinner Bradburn has been Scotland boss since 2014.
England rallied again, thanks to a 71-run eighth-wicket partnership between Moeen Ali and Liam Plunkett.
But Scotland's bowlers kept taking wickets and when pacer Safyaan Sharif had No 11 Mark Wood plumb lbw with seven balls to spare, England were 365 all out.
He said they had drawn additional inspiration from the involvement in their camp ahead of the match of Duncan Hodge, hero of the Scotland rugby team's Calcutta Cup win in 2000 when he scored all 19 of his side's win who is also a fine cricketer.
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Hussain interviewed Langer ahead of the series - watch the first ODI live on Sky Sports Cricket on Wednesday - who told him the team "would carry on sledging, but not resort to abuse".
"It is up to us to build on it. Hodgey said for too long Scottish sport has been about close misses and this could have been one of those days". It's good to play a high-scoring game under pressure.
Eoin Morgan's men are the top-ranked side in this format and, on a small ground with a flat pitch, Scotland's score did not look remotely safe as Jonny Bairstow thundered his way to 105 from 59 balls - becoming the first England batsman to register hundreds in three successive ODIs.
Nasser Hussain and David Lloyd joined Ian Ward to preview England's five-match ODI series against an Australia side attempting to alter its public image following the ball-tampering scandal.
SCORECARD MacLeod made 140 not out as Scotland surpassed their previous record total at this level of 341 for nine against fellow non-Test nation Canada at Christchurch four years ago.
Meanwhile, if England, who are without the services of Ben Stokes and Jos Butler can chase down this total then it will be joint second-highest successful ODI chase of all time.