Australia need a further 30 runs to take a first-innings lead in the second Test against New Zealand at the Adelaide Oval after closing day two on 241 for three.

Chasing the Black Caps' 270, the hosts put themselves in a strong position by stumps with Mike Hussey 69 not out and Michael Clarke unbeaten on 43.

Daniel Vettori bowled tirelessly over the final two sessions and finished with figures of one for 54 off 28 overs while Iain O'Brien took the important wicket of Ricky Ponting only minutes after the tea break and has one for 63.

Hussey and Clarke controlled the final session with some patient but stylish batting and have put on 86 for the fourth wicket.

Clarke strode to the crease and got off the mark with a textbook straight drive. Hussey also played some memorable strokes with his sweeping and pull shots a feature.

It followed the critical 106-run stand between Ponting and Hussey, which was the highlight of the second session.

The Australia skipper made batting look easy and smashed an amazing 11 boundaries by the time he reached his half-century.

But the Kiwis dried up the runs and he was out pulling a ball from O'Brien to mid-wicket where he was caught for 79 by the towering Peter Fulton.

Despite their later dominance, Australia made a shaky start to the run chase.

Matthew Hayden began his first knock in his 100th Test in style by hitting Chris Martin for a leg-side boundary but a combination of bad calling and ball watching saw him run out for 24.

The big Queenslander took off for a single but was stranded as Simon Katich stayed anchored at the non-striker's end.

In the morning session Brett Lee ripped through New Zealand's lower order to see the tourists bowled out for 270.

Lee took three for six in a 27-ball spell and finished with first-innings figures of four for 66 while Mitchell Johnson took the other day-two wickets and finished with two for 56.

A change of pace saw Lee dismiss the dangerous Brendon McCullum. He also had O'Brien caught behind before knocking Martin's middle stump out of the ground to deliver the number 11 another duck.

On day one, New Zealand had wasted opportunities to be 262 for six at stumps.

The Black Caps got on the front foot by reaching 101 for one at lunch, but from that point wickets fell at regular intervals.

Aaron Redmond's innings was a highlight with the opener bullying Nathan Hauritz in the opening session. He was eventually dismissed for 83 runs with 68 of his tally coming from boundaries and sixes.

McCullum and Vettori frustrated the Australians with a gritty partnership in the afternoon but there was little resistance once the stand was broken early on day two.