The Australian cricketers will resume on 35 for none on the third day of the second Test in Hamilton - a lead of two runs.
The New Zealand batsmen could only manage 264 all out for before tea in their first innings in reply to Australia's dismal 231 all out on the opening day.
Ross Taylor held the Black Caps innings together with the quickest century in New Zealand Test history off just 81 balls, surpassing Dan Vettori's record of a ton in 82 balls against Zimbabwe.
Taylor also hit three straight sixes and a four in one over off spinner Nathan Hauritz - the most runs ever taken off an Australian bowler in one Test over in the history of the game.
But after Taylor departed for 138, nicking one behind off Doug Bollinger, the tail failed to wag.
Tim Southee was the not out batsman on 22 - the Black Caps' third highest scorer. BJ Watling notched a respectable 46 while Vettori went for 15 and Brendon McCullum for a disappointing five.
Australia got to stumps without loss, before bad light halted play.