Moeen Ali's three-wicket burst reduced the tourists to a paltry 214 all out, before Eoin Morgan and Joe Root's 115-run partnership put the hosts on course for victory.
Morgan hit 69, with Root departing for 50, as England rode out a late wobble to start the five-match series in triumph.
Morgan, Root, Jos Buttler and Ali all perished to weak shots to leave bowlers David Willey and Liam Plunkett to finish the job.
Australia's first international action since March's ball-tampering scandal that saw Steve Smith, David Warner and Cameron Bancroft suspended ended in a defeat that would have been more comprehensive, save for England's errant batting.
Australia struggled for fluency throughout, feeling the injury absence of bowling trio Mitchell Starc, Pat Cummins and Josh Hazlewood just as much as their three suspended batsmen.
Moeen put England in control, claiming his first two wickets for three runs in a match-turning eight balls.
The Worcestershire off-spinner drew a false shot from Aaron Finch, clean bowled Shaun Marsh and then forced captain Tim Paine into a mistake to boot.
Glenn Maxwell hit 62 from 64 balls to dig Australia out of an even deeper hole, only to loft a facile catch to Jonny Bairstow off Plunkett.
England endured the worst possible start to their reply when Jason Roy fell to just the second delivery as he was late on his shot to a ball from Billy Stanlake that nipped back on him and was bowled without scoring.
Alex Hales and Jonny Bairstow then scored a flurry of boundaries before Michael Neser claimed his maiden one-day wicket when he trapped Hales on the back pad to have him lbw for five and leave England on 23 for two.
Bairstow continued to play freely as he went in search of a fourth consecutive one-day international century but he then pulled Kane Richardson straight to Travis Head at deep square leg and was caught for 28 to leave England 38 for three.
But Morgan and Root rebuilt the innings before Morgan and Buttler (9) fell to Andrew Tye as England leaked wickets throughout their facile run chase.
Root then edged Stanlake behind to depart on 50 when he ought to have steered England home.
Ali could not finish the job either, holing out off Michael Neser's bowling for 17, teeing up a tense finish with England seven down and still 18 short of victory.
But Willey sealed the win by thumping a huge straight six to end unbeaten on 35.
Related cricket links
