Wicketkeeper De Kock was promoted after Dean Elgar had to pull out of the test after injuring an ankle.
He had made the most of his opportunity. In between the edges and mishits, de Kock played handsomely through the onside and produced some nice drives.
Cook, a more natural, circumspect opener is a back foot player and had some close calls, notably when comprehensively beaten by left armer Trent Boult early on.
But he grafted hard and had a good reward at the interval.
New Zealand's four seamers all produced good deliveries, bowled with little luck, but did conceded a total of 18 boundaries in 28 overs.
Bracewell had de Kock dropped on 42, an inside edge to wicketkeeper BJ Watling which he couldn't hold with one glove. Watling had a poor morning with the gloves.
Wagner appealed for lbw against Cook on 36. It was rejected but had New Zealand referred the appeal to the third umpire, would have had Cook out, the replays suggesting the ball would have hit his leg stump.
At the toss there might also have been a small thought that better to bowl than risk a serious inquisition from South Africa's champion new ball pair Dale Steyn and Vernon Philander, who had put the top order through hoops before the rain arrived in Durban a week ago.
That's a kind of negative positive thinking and not one Williamson would espouse.
The bounce was too trampoline-like for the fast bowlers' liking and there was precious little pace in the pitch.
De Kock doesn't appeal as the sort of batsman who frets over what's just happened, switching his thoughts to where he might dispatch the next delivery. New Zealand needed to hit back hard in the second session of the series-deciding test.
New Zealand might not want to know the last four tests at Centurion have been won by the team batting first.
