Having opted to bat on a hard and bouncy track, Australia lost Phil Hughes - included in the place of the injured Shane Watson - for a quick 20, before Simon Katich and Ricky Ponting combined for a 79-run second wicket stand that saw the visitors past the luncheon interval.
Ponting departed soon after the break for 40, and Mike Hussey followed him back 11 runs later, to leave Australia at a sticky 115 for three.
However, Clarke entered and locked down with Simon Katich to grind out 70 runs in the 28 overs between lunch and tea against a disciplined local attack.
The break claimed another wicket as Katich could only add another five runs before becoming debutant Brent Arnel's second victim, trapped in front for 79 off 191 deliveries.
Clarke continued with Marcus North and after a measure and carefull start, brought up his fifty as he accelerated his innings into complete control, adding three boudaries and a launced six off Vettori inside four overs.
The second new ball did not deter Clarke and he continued to find the boundary to bring up his century with a tight single from the first ball of the last over of the day.
At stumps he has hit 10 fours and two sixes from his 142 balls,
and the upbeat partnership with North (52 not out) of 140 at almost
five an over sent the day Australia's way.
New Zealand: TG McIntosh, BJ Watling, PJ Ingram, LRPL Taylor, MJ Guptill, DL Vettori (capt), BB McCullum (wk), DR Tuffey, TG Southee, BJ Arnel, CS Martin.
Australia: PJ Hughes, SM Katich, RT Ponting (capt), MJ Clarke, MEK Hussey, MJ North, BJ Haddin (wk), MG Johnson, NM Hauritz, DE Bollinger, RJ Harris.