For England, who entered the showpiece event as the top-ranked side in ODI cricket, this was a second straight defeat after their shock 20-run loss to Sri Lanka.
The host nation, bidding to win a first World Cup title, can still qualify for the semi-finals but they are likely to need to beat at least one of India and New Zealand in their remaining two group games.
“There are teams that you have confidence playing against but I have had plenty of low scores against England as well,” said man-of-the-match Finch.
“It was nipping around first thing. We were as tight as we could be and then took advantage of any width.”
England’s reply saw them lose a wicket off just the second ball of their chase, with the struggling James Vince — only playing because Jason Roy was out with a hamstring injury — bowled by a Behrendorff inswinger.
Starc then took two wickets in nine balls.
Test skipper Joe Root was plumb lbw to an inswinger for eight before England captain Eoin Morgan (four) fell into a hooking trap when a top-edge was held safely by Pat Cummins at fine leg.
Australia, who had lost 10 of their previous 11 ODIS against England, were in complete charge with the hosts now 26-3.
England have surged to the top of the ODI rankings on the back of aggressive run-scoring but the worry for Morgan’s men is that too many of their top-order appear to know only one way to bat.
Jonny Bairstow, for example, fell next to a careless hook off Behrendorff before Stokes and Jos Buttler (25) repaired some of the damage with a fifth-wicket stand of 71.
Buttler was well caught by Usman Khawaja, running round and staying just inside the deep square leg boundary off Marcus Stoinis.
Stokes defiantly hit Glenn Maxwell for two sixes in three balls but, shortly before completing his fifty, the all-rounder pulled up with a calf injury.
Starc was brought back to take a key wicket and duly obliged with a thunderbolt yorker, his 18th wicket of the tournament, that ended Stokes’s 115-ball innings of 89, including eight fours and two sixes.
Stokes’s dismissal left England 177-6 in the 37th over and effectively ended the contest. Starc ended the match when he dismissed Adil Rashid.
Earlier Finch, dropped on 15, and fellow opener David Warner (53) came through some testing early overs to share a stand of 123 as too many of England’s pacemen, with the exception of Chris Woakes, dropped short.
The skipper’s exit sparked a late flurry of wickets but Australia had enough runs on the board.
Both Warner, the World Cup’s leading run-scorer, and Steve Smith were booed as they entered and exited the field following their recent return from year-long bans for ball-tampering.
Finch went to his century thanks to a misfield by Woakes but next ball he miscued a hook off Jofra Archer and Woakes held the catch at fine leg.
The skipper faced 116 balls, with 11 fours and two sixes in his second century of this World Cup following his 153 against Sri Lanka.