New Zealand finished the day on 38 for three, 443 runs behind South Africa's first innings total of 481 for eight declared.
In an era of rapid scoring in Test cricket, much of South Africa's innings was a return to a more attritional age, with the run rate hovering at around three runs an over.
Du Plessis was particularly cautious as he tiptoed to a fifth Test century off 225 balls.
It left New Zealand in deep trouble in a match which will decide the series after the weather-hit, abandoned first Test in Durban.
Also Read
Martin Guptill survived a sharp chance to Stiaan van Zyl at third slip off Philander when he was on four, with the ball bursting through the fielder's hands for four more runs. But he gave a more straightforward chance to the same fielder in Philander's next over without adding to his score.
It was clear that the ball had deviated off the batsman's trousers but only the faintest flicker on the ultra-edge device gave any indication that it had touched the bat first. But television umpire Richard Illingworth decided it was enough evidence to overturn his colleague's decision.
Taylor run out
==================
Du Plessis bemoaned the failure of his batsmen to convert good starts into big scores in the first Test and seemed determined to set an example against steady bowling on a pitch still offering some help to the seam bowlers.
A largely defensive innings included one extravagant shot which almost cost him his wicket. After labouring to 18 off 86 balls, he pulled a short ball from Trent Boult and the ball went for six through the hands of Henry Nicholls, running along the midwicket boundary.
It took South Africa 66 overs to add 198 runs to their overnight total of 283 for three. JP Duminy, 67 not out overnight, made 88 off 158 balls, with 13 fours, before he was caught behind off Tim Southee, getting a faint edge to an attempted pull against a bouncer.