Glenn Phillips has scored a test half century on debut but the Blackcaps have squandered a positive start on day three of the third test.
Nathan Lyon put Australia on track to finish off their perfect summer, going to stumps on day 40/0, leading New Zealand by 243 runs.
Lyon claimed his second five-wicket haul of the summer on Sunday to help to dismiss the Blackcaps for 251 in their first innings, in reply to Australia's 454.
It meant Australia took at least a 200-run first-innings lead for the fifth- straight time this summer, since the opening win in Brisbane against Pakistan.
Victory in Sydney will also mark just the 10th time they have whitewashed a home test summer, with the three-match series against New Zealand already wrapped up.
Sunday wasn't their most-dominant day but the Aussies had still landed an emphatic blow by the time David Warner went to stumps on 23 and Joe Burns 16.
Lyon finished with 5/68, by far his best figures on his home wicket that threatened to offer even more spin in the final innings.
He dismissed Tom Blundell before he could add to his overnight score of 34, with a shorter ball that spun between his legs and ricocheted onto the stumps off his pad.
The out-of-sorts Jeet Raval was trapped lbw for 31, wasting a review on the way as his poor summer continued.
The 32-year-old Lyon later returned to mop up the tail, bowling Will Somerville and Neil Wagner in quick succession for ducks.
His last wicket came in bizarre fashion, with Tim Paine using only one glove to stump Matt Henry after he blocked a ball and dragged a foot out of his crease.
Lyon could have had six had he taken his chances, dropping debutant Phillips twice off his own bowling.
Pat Cummins eventually bowled the rookie with an in-swinger on 52, after he also survived a life when he was caught off a James Pattinson no-ball.
Cummins (3/44) also claimed the scalps of Ross Taylor and stand-in captain Tom Latham, with the latter caught at mid-on for 49.
Mitchell Starc took one wicket, removing BJ Watling for nine when he played the ball onto his stumps.
But Colin de Grandhomme's dismissal would have frustrated the Blackcaps the most.
The allrounder perished trying to take on the arm of Matthew Wade as he attempted to return for a second run on 20, falling centimetres short.
It summed up New Zealand's afternoon, as a 63-run opening stand couldn't stop them being bowled out for less than 260 for the fifth-consecutive time on the tour.