England's spinners did most of the damage against an Australian team playing their first ODI match since the ball-tampering scandal which rocked the sport, resulting in bans for Steve Smith and David Warner, in addition to the resignation of coach Darren Lehmann.
The hosts made hard work of their run-chase target of 215, though, with Eoin Morgan needed to steady the ship and help them to a victory which keeps them top of the ODI world rankings.
A 115-run partnership between Joe Root (50) and Morgan (69) put England back in control of the contest, but they then lost three wickets for just 10 runs, with new Australia captain Tim Paine claiming the scalps of both Root and Morgan.
David Willey saw England over the line with an unbeaten 35, though, as the home side wrapped up the victory with six overs to spare.
The second ODI of the five-match series will take place in Cardiff on Saturday.