Still 127 runs behind with an entire day left to bat, the tourists' prayers initially looked as if they might be answered as more inclement weather and several wet patches on the pitch caused by rain leaking under the covers led to long delays.
When play did finally get underway three hours later than scheduled, England survived just one solitary over before Josh Hazlewood emphatically bowled Jonny Bairstow (14) with his first delivery of the afternoon that appeared to pitch on a damp spot before hitting off stump.
Off-spinner Nathan Lyon later accounted for the wicket of Moeen Ali (11) for the fifth time in the series, trapping the Worcestershire all-rounder lbw.
Dawid Malan, who made 140 in the first innings before his eventual dismissal sparked a collapse that saw England lose six wickets for 35 runs off just 51 balls, appeared to be Joe Root's last hope and he initially survived an lbw review after DRS showed that a ball from Hazlewood had pitched outside leg stump.
However, that reprieve lasted just a matter of minutes before the 30-year-old's latest determined knock ended on 54 when he was caught down the leg side by wicket-keeper Tim Paine off the bowling of Hazlewood, who sealed the sixth five-for of his Test career by having Craig Overton (12), struggling with a cracked rib, caught by Usman Khawaja at gully.
Stuart Broad had faced just one ball when he gloved a bouncer from Pat Cummins through to Paine for a duck to leave Australia within one dismissal of clinching victory in the five-match series. They completed their latest emphatic destruction of England's lower-order and triumphed by an innings and 41 runs when Chris Woakes was caught behind for 22.
Hazlewood finished with impressive figures of 5-48, while Cummins and Lyon bagged a brace each and Mitchell Starc claimed the wicket of James Vince on day four with what some have already dubbed as the "ball of the century".
Australia, after their previous wins in Brisbane and Adelaide, now travel to Melbourne for the Boxing Day Test with an unassailable 3-0 lead. They could potentially inflict another humiliating whitewash on England in Sydney early next month.
"It is very difficult to take," visiting captain Root said afterwards. "Fair play to Australia, they have outplayed us in three games. We have to be better. We've got to go to Melbourne prepare well and put in a really good performance there."
Australian counterpart Steve Smith, whose brilliant 239 earned him man-of-the-match honours, was understandably delighted to see his side reclaim the famous urn following their 3-2 defeat in England in 2015.
"It's nice to get recognition," he said. "I'm really proud of my performance in this game, to get my highest score and put in that partnership with Mitch Marsh, who I thought played magnificently. It set the game up for us after they got 400 in the first innings. I'm just so proud of the boys. The way we've been able to win this series, wrap things up in Perth and get that urn back, it's quite amazing."