Du Plessis’ fifth test century ensured South Africa were in a strong position even before seamers Vernon Philander and Dale Steyn grabbed a wicket each before stumps.
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Stand-in captain Faf du Plessis was batting on 57 at the break with Stiaan van Zyl yet to open his account in the final match of the two-test series at Centurion.
The brightest batting came in the morning when Cook and De Kock took South Africa to 100 for no wicket.
Nicholls was given not out by umpire Paul Reiffel but a South African review led to the decision being reversed.
Earlier South Africa were 437 for six at tea, with Du Plessis on 95 not out.
New Zealand are 38-3, having lost both openers and the in-form Ross Taylor.
But television umpire Richard Illingworth decided it was enough evidence to overturn his colleague’s decision.
Captain Kane Williamson (15 not out) and Henry Nicholls (4 not out) will be at the crease.
Du Plessis compiled a patient unbeaten 95 from 205 balls and will resume with Vernon Philander (six not out) as South Africa look to build a big first-innings total on a lively wicket that has both sideways movement and variable bounce. Knowing Duminy was paying special attention to rolling the wrists, he tested him with a short ball, Duminy pulled and the bottom edge gave BJ Watling an easy catch while denying Duminy a fifth Test century.
Temba Bavuma also fell to a short ball, top-edging a pull against Neil Wagner to be well caught by Doug Bracewell, running in from fine leg, for eight.
Neither of New Zealand’s swing kings Tim Southee or Trent Boult managed to take a wicket despite bowling 40 overs between them, and it was down to the inform Neil Wagner to give them some sort of relief as he picked up two.
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Van Zyl made 35 before being caught at a well-placed fly-slip by Taylor after edging an excellent Wagner delivery that was angled in from over the wicket but held its line. “It’s a bit of a fairytale thing, I’m quite amazed by it”, said Wagner, who spent several years playing and training with du Plessis. Taylor was struck twice, on the shoulder and arm, by lifting deliveries from Steyn and scored only one before pushing a ball from Kagiso Rabada to midwicket.
