Eoin Morgan had retire hurt following blow to head and never took field in the fifth ODI.
Finch and Bailey were unbeaten on 70 and 41 respectively as Australia won with 154 balls to spare.
Finch has hit nine boundaries and a six in his innings so far, as Australia were cruising towards their target.
Finch and Bailey were batting on 36 and 27 respectively at the end of 16 overs, with Australia cruising towards a win.
Smith edged a Mark Wood delivery to Jonny Bairstow to depart for a score of 12 off 28 balls.
Burns was caught by wicketkeeper Bairstow off the bowling of Willey.
Eoin Morgan was hit by a short ball from Australia left-arm fast bowler Mitchell Starc in the seventh over of the match.
Marsh and Hastings shared seven wickets between them as the hosts were steamrolled by the Australian pacers.
Brad Haddin feels his decision to miss the second Test put myself in a vulnerable position.
Ben Stokes was trapped lbw off the bowling of Mitchell Marsh for a score of 42 off 50 balls as England lost their seventh wicket with just 85 runs on board against Australia during the fifth and final One-Day International (ODI) at the Old Trafford in Manchester on Sunday. Marsh took his fourth wicket for...