Another victory at Nottingham on Tuesday would clinch the five-match series for England and erase the embarrassment of their recent loss to Scotland in their opening white-ball game of the summer.
With captain Eoin Morgan ruled out before the start of play with a back spasm, England needed Roy to come out firing and the opener responded with a century from 97 balls.
His departure, to a sharp catch from Tim Paine moments after the keeper had been cut on the face by a ball that reared up, did not check England's momentum and Buttler took up the charge, finishing the innings with a boundary.
Australia were left to chase what would have been their highest ever ODI winning total. Although debutant D'Arcy Short briefly prospered with 21, it was not until Marsh was joined by Ashton Agar (46) that he received proper support.
But after the pair put on 96 runs from 70 balls, Agar was smartly stumped off a Adil Rashid googly. Liam Plunkett then put an end to Marsh's superb innings on 131 from 116 deliveries to snuff out any lingering Australian hopes.
Plunkett ended with four wickets.
(Reporting by Neil Robinson, editing by Pritha Sarkar)
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