Australia's vice-captain bounced back from the media frenzy surrounding his relationship break-up to plunder his 14th test century and lead the tourists to an imposing 316 for four at stumps.
Clarke, 100 not out, and Marcus North, 52 not out, added an unbroken 140 for the fifth wicket and, on a pitch getting better and better, will have 500 in their sights today.
An impressive debut from 31-year-old New Zealand seamer Brent Arnel, who removed Phil Hughes, 20, with his fifth ball and later fellow opener Simon Katich for 79, meant the home side was in command at 176 for four but it slipped away fast in a hectic final session.
It was all about Clarke, after he quit the tour to spend a week in Sydney, then returned last Monday having split with high-profile model Lara Bingle.
"It [the century] was certainly better than being on zero.
"My first 10 runs took a hell of a long time today," he said.
"It's a very special feeling any time you make a hundred.
"It's been a tough couple of weeks, but the support I've had from family and friends, and the support from Lara as well has been tremendous.
"Without her support, I certainly wouldn't have been back over here."
Clarke was awful early on, taking 16 deliveries to get off the mark before reaching his half-century off 102 balls.
The next 50 took just 39 balls as he reached his century in the day's final over after hitting 10 fours and two sixes, raising both arms to acknowledge a generous ovation.
"I got to a stage about 80 when I said [to North] `I can't stop thinking about my hundred' and he said `if you see it mate, just hit it'.
"I played some horrible shots from 50 to 100 and I had a little bit of luck.
"I'm really happy I got there.
"I wouldn't have slept too much if I was on 98 or 99."
Arnel was the pick of the bowlers, seaming the ball both ways early on, although he suffered in the final session as batting became easier.
Chris Martin, one for 63 off 19 overs, took the only other wicket when his outswinger removed Michael Hussey for four.
BJ Watling did the honours there with a sharp catch at third slip, after he had run out captain Ricky Ponting, 41, with a direct hit from cover when the hesitant Katich pushed and ran.
When Arnel trapped Katich in front, ending a vigil of 261 minutes and 191 balls, New Zealand had a spring in its step. An outstanding middle restricted the tourists to 70 for two off 28 overs.
Captain Daniel Vettori homed in with 21 overs but could not snare a wicket, while Daryl Tuffey conceded just 35 off 16 but could not break through, and Tim Southee was expensive in conceding 55 off 13.
