Rory Burns and Zak Crawley logged the tourists' highest opening partnership of the five-Test series, advancing to 0-68 on day three of the series finale.
But England's bright start to their pursuit of 271 was followed by two hours of bumbling and bungling at Bellerive.
Joe Root's side lost 10 wickets in 22.4 overs to be all out for 124 and hand Australia a 146-run win.
Green, long regarded as Australian cricket's brightest prospect, was the catalyst for the chaos as the sun set on Sunday.
Ben Stokes gifted his wicket to Mitchell Starc, while embattled captain Joe Root's hopes of salvaging some pride were scorched by Scott Boland's unplayable shooter.
Root grinned in disbelief then threw his head back after the pink ball hit a crack and struck the bottom of off stump, knowing there was nothing he could have done to stall Australia's push for victory.
Nathan Lyon, who failed to deliver a single over for the first time in his 105-Test career, plucked a low diving catch in the deep to dismiss Stokes.
Cummins and Boland then sliced through the middle order and cleaned up the tail with remarkable ease, triggering jubilant celebrations.
Cummins threw the ball to Green as the belief of England, desperate to bank their first Test win in Australia since 2010-11, ballooned.
The allrounder, having delivered 44 wicket-less overs against India in his debut series, quickly captured the scalps of Burns, Crawley and Dawid Malan in a six-over spell either side of tea.
The 22-year-old also produced a nasty bouncer that kept low and struck Malan on the helmet as the No.3 batter tried to take evasive action.
There was a lot of pre-series talk about it being unfair to compare Green with Stokes, yet the reality is the young gun has outperformed England's talismanic allrounder with bat and ball this series.
Green's inspired spell came on the same day he scored 23 while adding 49 runs alongside Alex Carey, sharing Australia's best partnership in a slapdash second-innings total of 155.
Carey scored 49 and stood up as express paceman Mark Wood snared career-best figures of 6-37, top-scoring with some help from a divisive decision by third umpire Paul Reiffel.
Carey was on 19 when he chopped on, only for Chris Woakes' delivery to be judged a no-ball after Reiffel studied every angle possible.
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