Josh Hazlewood has risen to the challenge of Australia's pace spearhead but the weight on his shoulders could be about to grow after an injury scare to Peter Siddle.

In another blow to Australia's depleted pace stocks, Siddle was off the ground for long periods of the final session on Sunday due to back spasms.

Siddle's absence, however, has not halted Australia's push for victory in the first Test. The visitors could have the match wrapped up as early as Monday after another fruitful day in Wellington.

They require six more wickets to go one up in the two-match series which would leave them needing only to draw next week to regain the No.1 Test ranking.

New Zealand finished the third day on 4/178, still 201 behind Australia, and they will be doing well to avoid an innings defeat.

Siddle has bowled only eight overs in the second innings. It is the third time this summer Siddle has been dogged by niggles. He battled a back problem during the day-night Test then spent more than a month on the sidelines after hurting his ankle during the Boxing Day Test.

His availability for the fourth day will hinge on how he responds to medical treatment but Australia's team management are hopeful he will be fit.

"It's a bit of a back spasm and they're never nice," Adam Voges said after play on Sunday.

"We've got some good medicos who will look after him tonight and we're hopeful he'll be out there tomorrow.He's got very good skills with the reverse swinging ball so hopefully we'll see him out there tomorrow."

Australia's pace ranks are already thin with James Pattinson unable to play this match due to concerns over his ability to last the full game. He is not considered a certainty for the second Test.

The Kiwis were dealt a hammer blow late by Mitchell Marsh, who claimed the wicket of crowd favourite Brendon McCullum with the final delivery of the day.

Victory, however, is unlikely to be gifted to the Australians. The Kiwis showed far more purpose with the bat on Sunday than they did two days earlier, though conditions are now much easier for batting. The time for real application was Friday.

Hazlewood is revelling with the added responsibility of being Australia's pace leader. While Nathan Lyon claimed the spoils with two wickets, Hazlewood was the most penetrating member of the Australian attack.

The giant paceman claimed the prized scalp of Kane Williamson, who was near unstoppable in November but now finds himself in a form trough.

Williamson was dismissed for 22 after an engrossing contest with Hazlewood. He has passed 50 on only one of his last seven innings against Australia.