Nathan Lyon took five for 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 0-2 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.

“It’s always special being part of the Sydney Test match and playing in front of your family and friends, and to perform in the first innings was pretty special,” Lyon said.

“There’s still plenty of work to do in the second dig ... but if you were rocking up today and saying we’d end up with a lead of 240 and 10 wickets in hand, we’ll take that every day,” he added.

Henry batted despite breaking the thumb on his non-bowling hand on Day I 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.

“It was a really enjoyable time out there,” Phillips said. “It’s a shame I wasn’t able to go on and extend the innings a bit, but that’s cricket.”