Williamson equalled the Kiwis record for test centuries as his side reached 321 for four at the close of day three of the third test against South Africa in Hamilton on Monday.
A solid start from New Zealand to finish the day on a high and snatch the advantage even, after de Kock had rallied along with the lower order to take South Africa to 314.
South Africa were 123 for four at stumps on a rain-shortened first day of the third Test against New Zealand in Hamilton on Saturday.
Quinton de Kock fit to play in deciding third Test, but New Zealand will be without Boult, Southee and Taylor.
Keshav Maharaj took a career best six wickets as South Africa beat New Zealand by eight wicket and go 1-0 up.
Bavuma, de Kock fall just short of centuries but South Africa takes 81-run lead at stump on second day.
The Blackcaps take two late wickets to continue fightback after Nicholls ton takes hosts to 268.
Southee confirms his return and Broom set to debut with Boult and Taylor injured.
Rain played spoilsport as the first cricket Test between South Africa and New Zealand ended in a draw at the University Oval here on Sunday.
New Zealand captured the key South African wicket of Dean Elgar late on day four to keep the faint prospect of a result alive in the first Test in Dunedin on Saturday.