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Chasing 354 runs to win, England were bowled out for 233, which saw their last six wickets going for just 57 runs in the historic day-night affair.
Left-arm paceman Mithcell Starc ran through the English batting middle order, after Josh Hazlewood scalped both Joe Root (67) and Chris Woakes (5) in his first two overs of the day without addition to their overnight scores.
Thereafter, the Australians took the game by the scruff of its neck with Starc accounting for stumper Jonny Bairstow (36), Craig Overton (7) and Stuart Broad (8) while off-spinner Nathan Lyon added to the woes with the wicket of Moeen Ali.
Resuming the day at 176/4, the tourists failed to provide any resistance as they kept losing wickets at regular intervals to completely lose the plot.
England could surrender the Ashes next week at the WACA ground in Perth, where it has not won a Test since 1978.
Delighted at the win, Australia skipper Steven Smith said: "We always had the faith in the team and the belief.
"We thought if we could come out and bowl well this morning, hit our lengths and get one or two wickets, then things can happen quickly," he added.
Root was understandably disappointed, but still positive as he looked ahead to a come-from-behind series win.
" I don't think we did ourselves justice," he said.
"We're still massively in the series. We showed that from the way we played yesterday. That has to be the benchmark how we approach the rest of the series," he added.
Both the sides will now face off in the third Test at the WACA in Perth from December 14-18.