Australia piled further misery on New Zealand as Nathan Lyon's five-for helped roll the Black Caps and extend the home side's advantage on day three of the third Test.

Lyon overcame a bloodied thumb and two dropped catches to claim figures of 5-68 in Sydney, where the embattled Kiwis were dismissed for 251 on Sunday.

After skittling New Zealand late in the final session, David Warner (23 not out) and Joe Burns (16 not out) guided Australia to 40-0 and a lead of 243 runs at stumps.

New Zealand returned to the SCG at 63-0, with Tom Latham and Tom Blundell at the crease in reply to Australia's 454, however, it was another difficult morning for the tourists.

Lyon bowled Blundell before the New Zealand batsman could add to his overnight score of 34 and the Australia spinner struck again – trapping Jeet Raval (31) lbw.

Pat Cummins (3-44) joined the wicket-takers in the following over when his delivery to stand-in captain Lathan (49) was caught by Mitchell Starc as the Black Caps were 141-3 at lunch.

Debutant Glenn Phillips dug deep for New Zealand, who have tried to restore some pride having already lost the trans-Tasman series, but he had little support in the middle session.

Cummins trapped Ross Taylor (22) lbw, BJ Watling (9) was bundled over by fellow paceman Starc and Colin de Grandhomme (20) was run out prior to tea.

Phillips, who was twice dropped by Lyon, celebrated a half-century before he was bowled by Cummins, with Lyon cleaning up the tail – William Somerville (0), Neil Wagner (0) and Matt Henry (3) sent back to the pavilion.

That brought Australia out to bat again, and Warner and Burns negotiated a tricky 16-over spell to put the hosts firmly in control ahead of the penultimate day.