In the first match at the new Perth Stadium, the tourists set Australia 260 to win in front of a record West Australian cricket crowd of 53,781.
Despite resting frontline bowlers Chris Woakes and Mark Wood, and having quick Jake Ball struggling with illness, the tourists managed to defend their total.
Young seamer Tom Curran was the match-winner with five wickets as Australia were dismissed for 247 with 10 balls remaining.
England, beaten 4-0 in a lopsided Ashes Test series, bounced back to claim the limited-over series 4-1.
"We thought we'd pulled it back really well, but we didn't start well with the ball -- been a bit of trend," he said.
"Again we lost wickets in clumps and you can't do that. Our batting again wasn't good enough, these lapses are happening way too often in one-day cricket."
Australia, thanks largely to Marcus Stoinis who was promoted to number three and made 87, looked to be cruising to victory on 189 for four.
Curran returned to the attack and removed Glenn Maxwell (34) and Mitchell Starc (0) in the space of three balls as Australia lost their way.
When Tim Paine and Adam Zampa threatened to snatch the match with a gritty ninth-wicket stand, Curran came back into the attack and clean-bowled the latter with his third ball.
In just his third one-day international and his first of the series, the 22-year-old then delivered the last rites by bowling Paine for 34.
Curran finished with 5-35 and also had two catches dropped from his bowling, both by the normally reliable Jonny Bairstow.
"Watching the boys play one-day cricket recently has been a pleasure and to come in and try and take my chance is a great feeling," he said.
"I've been training hard. To come and play the first one-day international at this unbelievable stadium, in front the Barmy Army... the game was unbelievable, what a finish."
Moeen Ali's horror tour with the bat continued when he went cheaply in the English innings. But he claimed 3-55, including the crucial wickets of Smith (12) and Mitch Marsh (13) -- the latter falling to a superb reflex return catch.
Test captain Joe Root made a typically busy 62 but the English appeared to have fallen start after a flying start when they were bowled out for 259 in 47.4 overs.
The English openers blazed away early in a polar opposite to their nightmare start in Adelaide on Friday.
In that game they were 5-8 and went to suffer their first defeat of the series, but there were no such problems on Sunday.
Jason Roy led the charge and enjoyed some good fortune when he was brilliantly caught behind by Paine off Starc, only for it to be ruled a no-ball.
A number of England batsmen made similarly good starts but only Root went on to make a significant score.
Much to the delight of the crowd, Tye was the star with the ball, cleaning up the English tail to finish with 5-46 off 9.4 overs.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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