Eventually it was left to Jos Buttler, unbeaten on 54 from just 29 balls, and Alex Hales, with 34 not out, to hurry them home to another win.
The world champions need to avoid defeat at Old Trafford on Sunday to prevent a first ever whitewash by England in a series of five matches or more, after a six-wicket loss to Eoin Morgan's side in Durham on Thursday.
After piling up a world record total of 481 from a 50-over global at Trent Bridge on Tuesday and inflicting Australia's heaviest-ever defeat, England again outplayed the visitors, pulling off their second-highest ever ODI run chase.
England followed Tuesday's world record 481-6 at Trent Bridge by demonstrating they can be equally unstoppable in the chase.
Roy mixed the odd lusty blow with numerous eye-catching drives through the off side - including one sumptuous four off the back foot through point - while Bairstow played the most delightful straight drive as he motored along in Roy's slipstream.
Roy raced out of the blocks at the start of England's chase, dominating the strike to post his 13th ODI fifty off 36 balls with the help of some crisp driving and top-edged hook for six off Billy Stanlake. Five matches were played during this series, this was the third match.
While Finch had given the Australia the start they desperately needed, it was Shaun Marsh who anchored the innings in brilliant fashion before his dismissal. "Most notable of these was the sight of Tim Paine dropping the most straightforward of catches in the England innings". It is possible to fit Jason Roy, Jonny Bairstow and Hales in the same team. With Roy, Bairstow and Hales in such good nick, England now have a top three to rank with any in the world although Morgan admits he is not looking forward to the selection meeting when Ben Stokes and Chris Woakes return from injury. Conditions in England make seamers pretty important and with the kind of tracks that are being churned out, Australia might want to look for bowlers who take wickets rather than ones who rely on containment, something which seems impossible in England these days.
"I've got massive respect for England and the way they are playing their cricket", added Langer.
It was, in fact, the first wicket Australian bowlers could snatch in the innings. We'll look after them.
"But the silver lining is that we're building a lot of depth, we're exposing a lot of players that at any other stage may not get an opportunity at all". The batting unit is okay, but they will get another go for this ODI.
"I think we've still got to stick to our strengths, but just find a way to stay in the contest for longer", Finch added, after Australia's 15th defeat in 17 completed ODIs.