Nathan Lyon took 5-68 as a dominant Australia dismissed New Zealand for 251 before the home batsmen took over to extend their lead to 243 by the close of play on the third day of the third and final test on Sunday.
Already 2-0 down in the series after thumping defeats in Perth and Melbourne, New Zealand have been ravaged by illness and injury and now face a huge battle to avoid a third heavy loss before they head home.
The Sydney Cricket Ground was turned pink for the 12th straight year in aid of cricketing great Glenn McGrath's breast cancer foundation but there was nothing charitable about Australia's approach to the match.
Openers David Warner (23) and Joe Burns (16) steered the hosts to 40 without loss at stumps to add to the first-innings tally of 454 built on the back of Marnus Labuschagne's maiden double century.
It was the Australian bowling attack, though, that once again set the tone as they took all 10 New Zealand wickets for the fifth time in the series.
Off-spinner Lyon carried the ball off the pitch to huge applause an hour after tea after he had Matt Henry stumped to end New Zealand's innings and secure the 17th five-wicket haul of his career, his first against the Black Caps.
Henry batted despite breaking the thumb on his non-bowling hand on day one of the match, the latest in a catalogue of misfortune that robbed the tourists of captain Kane Williamson and a string of other top players.
Glenn Phillips, flown over from New Zealand on the eve of the test to cover for the sick Williamson and Nicholls, offered the most resistance with a 52 on his test debut.
The 23-year-old enjoyed some luck when he was dropped twice by the normally reliable Lyon and again just before tea when he was caught in the deep off a James Pattinson no-ball.
He brought up his maiden half-century with a brilliant pull shot through square but two balls later was clean bowled by paceman Pat Cummins, who took 3-44 to show once again why he is the world's top-ranked test bowler.
Lyon tops a few lists of his own these days and it was the unassuming off-spinner who broke New Zealand's early resistance after they had resumed on 63 without loss.
He bowled opener Tom Blundell for 34 and trapped Jeet Raval leg before wicket for 31 in the first session and returned after tea to send back tailenders Will Sommerville and Neil Wagner, both for ducks, in a magnificent two-wicket maiden.
Conditions were much cooler than on Saturday's second day but there was a distinct smell of smoke in the air from the bushfires that have been raging around Sydney for the last couple of months.