Lunch Australia 383 and 113 for 4 (Green 17*, Head 24*) lead New Zealand

Nathan Lyon fell short of a maiden Test half-century, but Australia's lead grew past 300 after Cameron Green held firm and Travis Head counterattacked to thwart New Zealand's attempts at a comeback early on day three at Basin Reserve.

In windy and overcast conditions, Usman Khawaja was also dismissed for 28, but Australia remained in control of the first Test as their lead hit 300 when Green smashed the spin of Glenn Phillips for six just before lunch.

After his brilliant unbeaten 174 in the first innings, Green has looked solid while Head, who had made one run in his last three innings, loomed ominously after the interval having thumped 24 off 26.

Lyon, the nightwatcher, dominated the first 30 minutes of play to frustrate a New Zealand team desperate for early wickets. Having scored the most runs in Test history without a half-century, with a highest score of 47, Lyon fell short after making a breezy 41 off 46 balls.

Even though they bowled better as the session wore on, New Zealand's hopes of a rare Test victory over Australia look forlorn with the highest ever run chase at Basin Reserve being 277 for 3 by Pakistan in 2003.

The surface has not flattered out, as is often the case mid-match at Basin Reserve, but batting has seemingly become a bit easier than on the opening couple of days. Australia will be keen to move the game forward with showers forecast on day five.

New Zealand endured a torrid day two with bat and ball to fall well behind in the contest. But they hoped the momentum built over the late wickets of Steven Smith and Marnus Labuschagne could spill into a crucial day three.

New Zealand, however, were quickly left flustered much like what they experienced 24 hours earlier when Green and Josh Hazlewood produced a record 116-run last-wicket partnership.

Lyon had survived a tough period late on day two, where he copped a blow to his body and was dropped on the last ball of play by Tim Southee in the slips. But he looked more comfortable after Australia resumed at 13 for 2. He dominated the strike and rode his luck to edge Southee through the slips in the first of three boundaries in a row.

Australia's lead passed 250 and Lyon notched 1500 career runs as he cashed in on wayward New Zealand bowling. Much like when they went through the motions against Green and Hazlewood, there was a lack of hostility from New Zealand's quicks who mostly resisted bowling short.

But Lyon was unable to reach his milestone after he whipped Matt Henry to a leaping Will Young at midwicket.

A relieved New Zealand then settled and bowled with discipline as Australia slowed to a crawl despite Green starting with a flowing drive through the covers reminiscent of his masterful century in the first innings.

Without a frontline spinner after Mitchell Santner was overlooked, Southee turned to Phillips who had Khawaja stumped in sharp glove work by Tom Blundell. Will O'Rourke also provided a spark for New Zealand with potent short of a length bowling, but Green remained resolute as he continued his outstanding match.