It was a fairytale end to their Australian tour and because the win gave the English an unbeatable 2-0 lead in the best-of-three tri-series finals after their four-wicket victory in Melbourne on Friday, the third game will not be played.
England, led by Paul Collingwood's third successive man of the match performance, made 246 for eight after winning the toss and electing to bat and then emerging swing bowler Liam Plunkett starred with the ball as Australia struggled to 152 from eight from 27 overs in reply.
When rain brought a premature end to the match, an outclassed Australia were well short of the necessary total of 187 under the Duckworth-Lewis system, following earlier rain delays.
It was England's second win in the tri-series and their first since 1986-87.
England started the tri-series as 14-1 rank outsiders, were told by the Australian media they might as well go home after two poor performances in Adelaide and finished the series without injured quartet Kevin Pietersen, Michael Vaughan, James Anderson and Jon Lewis.
Yet they won their last four games to snatch an unlikely trophy from the wreckage of their previously disastrous Ashes tour as Australian coach John Buchanan's complaints that the English were not providing enough competition for his side came back to haunt him.
It was the first time Australia had not won their home tri-series since 2001-02 and they looked like anything but a side heavily favoured to win a third World Cup in succession in a couple of months.
It was the first time the Australians had lost three games in a row on home soil since 2002.
After Collingwood made 70 to help England post a total that was always going to be competitive at a ground where teams batting first have an excellent record, Plunkett (3-43) turned the game on its head in the first over after the day's third rain break.
Australia were already in some trouble at 39-2, with Plunkett having claimed the prized wicket of Australian captain Ricky Ponting, when the rain came.
With the first ball after the resumption, things got much worse for the home side when Plunkett went around the wicket and produced a huge inswinger to clean bowl the dangerous Adam Gilchrist.
Plunkett struck again to have Michael Clarke caught behind from the last ball of what was a pivotal over as Australia slumped to 40 for four.
Interim captain Andrew Flintoff, who would have savoured the victory more than most after a draining summer, then came into the attack and snared the one player who might have been able to engineer an Australian comeback, the normally reliable Mike Hussey, for a duck.
There was more drama when rain forced the players off for a fourth time, with Australia at 79-5 and 3.4 overs still needed in the Australian innings to constitute a match.
All hope of an Australian revival disappeared when James Dalrymple hauled in an incredible one-handed diving catch from the bowling of the irrepressible Collingwood to remove Shane Watson for 37.
Collingwood also claimed the scalp of Brad Hogg to cap an outstanding finals series.
Earlier, Collingwood's rich vein of form continued when he top-scored to ensure his side made a total that would challenge the Australians at a ground where recent one-day history has strongly favoured the side batting first.
Collingwood and Flintoff put on 97 for the fifth wicket to steady an England innings that was not helped by poor running between the wickets.
Collingwood was coming off successive centuries and again batted with great assurance, making a chanceless 70 before being caught behind attempting a cheeky reverse sweep off seamer Nathan Bracken (2-38).
Flintoff made 42 before falling to a freak return catch by fast bowler Brett Lee.
The England allrounder sweetly struck a drive, but Lee took a superb reflex catch in his follow through.
The last over of England's innings was fittingly bowled by veteran Australia pace bowler Glenn McGrath, in his last game for his country at his home ground.
McGrath (2-41) sent the crowd into raptures when he claimed a wicket with his last ball, Paul Nixon caught by Hodge on the midwicket boundary for six.
England 246 for 8 in 50 overs (Paul Collingwood 70, Mal Loye 45, Andrew Flintoff 42, Ian Bell 26; N Bracken 2 for 38, McGrath 2 for 41, Brett Lee 1 for 53) beat Australia 152 for 8 in 27 overs (Brad Hodge 49, Shane Watson 37, Gilchrist 20; Plunkett 3 for 43, Collingwood 2 for 26, Flintoff 1 for 10) by 35 runs (by virtue of D/L method)