At the Basin Reserve, Philander and Morne Morkel put on 57 for the final wicket to take them to 359 in the first innings after they had struggled at 94 for six. It swung the game, given New Zealand lost their last four second innings wickets for 16 runs in 35 balls on what was considered a sound batting pitch.
New Zealand bowling coach Shane Jurgensen conceded South Africa had exhibited a more robust batting tail.
"They've got solid techniques, they got a few away today and we probably didn't execute as well as we wanted.
"They've had some luck, but they can certainly bat. They've won the battle of the lower orders so far, but ours has an opportunity to make that up with three days to go."
South African batting coach Neil McKenzie said his lower order had returned their set targets.
"We place a high emphasis on your wicket, so you're not a gift, and all the guys have responded well.
"They've been working hard against the short ball and spin. The wickets are a touch slower here so the short ball isn't as threatening as it might be elsewhere. That offers them more confidence."
De Kock was also credited as a batting chaperone.
"[Australia's Adam] Gilchrist used to do that," McKenzie said. "You knew if he stayed there for an hour he'd have 30-40 runs and in a partnership that makes more.
"It's about getting him out rather than keeping him quiet."