Labuschagne hits fourth ton as Australia take charge in Sydney
With the series already lost after heavy defeats in Perth and Melbourne, the Black Caps were rocked when Williamson, batsman Henry Nicholl and spinner Mitchell Santner were ruled out of the match by a flu virus.
Marnus Labuschagne scored his fourth century in five matches as Australia dominated a New Zealand side ravaged by illness and missing captain Kane Williamson to reach 283 for three on the first day of the third and final test on Friday.
With the series already lost after heavy defeats in Perth and Melbourne, the Black Caps were rocked when Williamson, batsman Henry Nicholl and spinner Mitchell Santner were ruled out of the match by a flu virus.
Australia had never needed an invitation to plunder runs over this series and the makeshift New Zealand attack was duly put to the sword on a mostly sunny day when the smoke from the bushfires stayed away from the Sydney Cricket Ground (SCG).
Labuschagne looked immovable as he hit a magnificent 130 not out to add to the innings of 185 and 162 he registered against Pakistan in November and the 143 he scored against New Zealand in the first test.
The 25-year-old piled on the runs in a third-wicket partnership of 156 with Steve Smith (63) and will resume on Saturday with Matthew Wade, who had scored 22 not out off 30 balls by the close of play.
"It's rare that you play an away team with five changes but that's the circumstances they have with the sickness," said Labuschagne.
"It was a nice day out there and a good day for Australia ... I'm just trying to keep it in the moment, just focus on each ball."
Tom Latham was named New Zealand captain in Williamson's absence and his first act was to lose a toss the tourists would have been desperate to win after selecting two spinners and dropping paceman Tim Southee.
With Southee's usual strike partner Trent Boult ruled out by injury, New Zealand started a test for the first time in more than a decade without one of the pair or Williamson in the side.
Colin de Grandhomme, who took the new ball with Matt Henry, played a part in all three wickets to fall, first having opener Joe Burns caught in the slips off an outside edge for 18.
David Warner departed for 45 three balls after lunch when quick Neil Wagner fired a delivery down the leg side that the Australian opener steered to gully for de Grandhomme to take a fine catch.
Wagner has dismissed Smith four times in four innings this series and the former Australia captain was so determined not to make it five that he took 39 deliveries to get on the board.
The biggest cheer of the first two sessions came when Labuschagne tore off down the wicket for a hurried single that finally got Smith off the mark.
Labuschagne had a nervous spell on 99 but a four, his eighth, to fine leg finally got him to the century mark for the fourth time in 14 tests.
Smith eventually fell to de Grandhomme and the second new ball, the world's second ranked test batsman clearly furious with himself after leaving his bat out and watching the ball ping off it and into the hands of Ross Taylor at first slip.
