The historic triumph, despite a gutsy England fightback, means Australia have retained the Ashes urn for the first time on English soil since 2001.
England had entered the final day with a gargantuan task of batting out the 98 overs for a draw to keep the series alive but were eventually undone by extraordinary bowling from Pat Cummins and Josh Hazlewood.
The resolve shown by England's tail-enders to survive the last session was reminiscent of the side's miraculous win at Headingley in the previous game.
But the self-assured Craig Overton was dismissed by Hazlewood for 21 to give Australia a hard-earned victory after battling throughout the day.
Australia now head into the last game of the series with a chance of accomplishing their first Test series win in 18 years.
England's splendid rearguard effort was spearheaded by Jos Buttler earlier in the day when he faced 111 deliveries for his 34 runs.
Buttler, unnerved by the mammoth task at hand, was deceived as he shouldered his arms to a sharp in-swinging ball from Hazlewood that knocked the top of off-stump.
The absorbing contest then further tilted in Australia's favour when Jofra Archer was pinned lbw by off-spinner Nathan Lyon.
With still two hours to go till the close of play, England's hopes of salvaging a draw reignited with Jack Leach and Overton showcasing glossy defence.
But the stubborn pair was uncoupled by part-timer Marnus Labuschagne, who turned one from the rough outside off-stump to tickle the inside edge of Leach's bat as the ball looped to Matthew Wade at short leg.
The template for Australia's dominance in the match was drafted by Steve Smith's spectacular batting heroics.
The star batsman perpetuated his extravagant run-spree with a double century in the first innings before accumulating a counter-attacking half-century on the fourth day when his side languished at 44-4 at one stage.
Smith's ninth consecutive fifty-plus score against England has now taken his tally for the series to 671 runs at an astonishing average of 134.2 comprising three hundreds.
The world number one Test batsman had to sit out the third game due to his concussion injury received from a blow to the neck from an Archer bouncer but he has still managed to top the run charts this year.
While the hostile English crowd has routinely booed Smith, reminding him of his involvement in the ball-tampering scandal last year, the 30-year-old defied the mocking chants with stunning batting displays.
England began the fifth day undamaged going through the first hour without losing a wicket.
However, two quick strikes including the wicket of Headingley hero Ben Stokes left England floundering at 74-4 at lunch.
World Cup-winner Jason Roy, who has not yet replicated similar levels of success in the red-ball format, curbed his natural attacking instincts but was dismissed off a fine off-cutter from Cummins to ping the stumps.
Later, Stokes had to depart immediately for a score of one as he edged the ball to wicketkeeper Tim Paine to hand Cummins his fourth wicket of the innings.
England, who haven't been able to bat out the fifth day for a draw for six years, were further derailed as Joe Denly was out for 53 by a vicious off-break from Lyon.
Jonny Bairstow briefly resisted the Australia bowling attack before being dismissed for a second time in the match by Mitchell Starc.
Although Smith earned all the accolades for his stupendous form, Cummins' seven wickets in the match were equally crucial for setting up Australia's win.