The first two triumphs came under John R Reid in the 1961-62 summer. The third win came on the 1994-95 post-apartheid tour and the most recent occurred in 2003-04 courtesy of 11 wickets for 180 from man-of-the-match Chris Martin.
New Zealand have returned four draws and nine losses since.
Williamson's talisman-like role will be crucial to altering that flow.
A test average of 50.07 from 106 innings suggests he is the man to effect change, although that mean drops to 35.06 from 12 innings against the Proteas.
Batting against South Africa's pace attack is among the toughest of cricketing challenges.
Even in a Steyn-less side, eking out an existence against Kagiso Rabada, Vern Philander and Morne Morkel will require levels of concentration and responsibility akin to those of an airport traffic controller.
A case of cricketing Survivor looms. To quote the television show's mantra: Can Williamson "Outwit, Outplay, Outlast" his opponents?
Rabada delivers stamina and pace; Philander delivers accuracy and ruthlessness; Morkel delivers bounce and consistency.
To underline the task, Rabada welcomed a return to the longest form after the ODI series.
"One-day cricket requires a lot of skill. There's so many plans: wide yorkers, slower ball bouncers, yorkers upfront, back of the hand slower balls, but with test cricket I don't think you will need that many [plans] so you have less of a headache.
"Test cricket is going to affect you more in terms of patience and perseverance, which can be quite mentally draining. You can be out on your feet in the field and you have to adjust and take things at a slower rate."
That's what the New Zealand captain has to hope for.
He wouldn't be drawn on how his batting would affect this series, deferring to the team's requirements instead.
But make no mistake.
His mental durability, and that of all the New Zealand batsmen, is set to undergo an exhausting exam.
