Roy's innings and a typically quickfire 91 not out from stand-in captain Jos Buttler, deputising after regular skipper Eoin Morgan suffered a back spasm shortly before the toss, took England to a total of 342 for eight.
Roy, dropped by England for last year's Champions Trophy semi-final on this ground, was back at Sophia Gardens less than two weeks later in a Twenty20 global against South Africa.
This defeat was Australia's seventh in eight ODIs but the form of Marsh was some consolation.
Buttler previously led England during a series win in Bangladesh in October 2016 when Morgan refused to tour because of security concerns.More news: Rapper XXXTentacion reportedly shot in Florida
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But, Marsh finally found some support from Glenn Maxwell (31) and Ashton Agar (46), sharing a 96-run partnership with the latter, and going through to his own 95-ball ton, that had Australia threatening to pull off an upset win.
Australia are missing several key players, with star batsmen Steve Smith and David Warner serving year-long bans for their roles in March's ball-tampering scandal in Cape Town, while Ashes-winning fast bowlers Mitchell Starc, Pat Cummins and Josh Hazlewood are all injured. We couldn't quite finish it off at the end there. "I wouldn't say being dropped in that Champions Trophy has anything to do with making any hundred feel any better than the next. When I wanted to start expanding my game, unfortunately I got out - but I was still happy". Meanwhile Buttler said: "I felt in good touch today.If we are being brutal, we can be more polished in the field".
With the Socceroos having been beaten by France at the World Cup and the Wallabies losing on home soil to Ireland, the nation's cricketers could not lift spirits by levelling up the five-match series. "Obviously, we had that hiccup against Scotland, and then the first game (of this series) I was a bit panicky, a bit wary of where my game was at", Roy admitted.
The first rain break came when Roy was on 66 not out.
Roy was eventually dismissed during an eventful 36th over.
The wicket England needed came when Plunkett bowled Marsh with a full delivery to leave Australia 293 for eight. But next ball he was out when Tye took the edge and Paine held a superb one-handed catch as he dived to his left.