The other 12 to the full set include some of the great batting names of the last generation.
Three Australians, Steve Waugh, Adam Gilchrist and Ricky Ponting; and three Sri Lankans, Marvan Atapattu, Sangakkara and Mahela Jayawardene have climbed that mountain along with two celebrated Indians, Sachin Tendulkar and Rahul Dravid, and two South Africans, Gary Kirsten and Jacques Kallis.
Pakistan's Younis Khan and West Indian Brian Lara complete the list.
By lunch New Zealand, who had started the second day of the second test at 329 for two, were simply ramming home their advantage, with Ross Taylor and BJ Watling, fresh from their 253-run stand in the first test on the same ground a week ago, on 50 and 18 respectively.
It was Taylor's 25th test 50 and he looked well set to make it back-to-back centuries in the series.
Williamson, having written himself into the history books again - and taken his test average to 50.48 - slapped a sharp catch to Craig Ervine at gully off seamer Michael Chinouya.
Then lefthander Henry Nicholls tried to sweep Zimbabwe legspinner Graeme Cremer, missed and went lbw for 15.
In six test innings since his debut against Australia last February, Nicholls has reached 20 just once.
Taylor overtook his mentor Martin Crowe's mark of 5444 test runs and now has only Stephen Fleming (7172) and Brendon McCullum (6453) in front of him.
The pitch was still totally in the batsmens' favour and New Zealand were shutting the door on the hosts.
New Zealand won the first test on the same ground by an innings and 117 runs.
Kane Wlliamson's century record in tests:
3 v Sri Lanka: 135, Colombo 2012; 242 not out, Wellington 2015; 108 not out, Hamilton 2015
2 v India: 131, Ahmedabad, 2010; 113, Auckland 2014
2 v West Indies: 113, Jamaica, 2014; 161 not out, Barbados, 2014
2 v Australia: 140, Brisbane 2015; 166, Perth, 2015
1 v Pakistan: 192, Sharjah, 2014
1 v Bangladesh: 114, Chittagong 2013
1 v England: 132, Lord's, 2015
1 v South Africa: 102 not out, Wellington, 2012
1 v Zimbabwe: 113, Bulawayo, 2016