South Africa were 437 for six at tea, with Du Plessis on 95 not out.
Apart from a burst of scoring immediately after lunch, it was slow going for Du Plessis, who had faced 205 balls by tea, hitting ten fours and two sixes.
The South African captain bemoaned the failure of his batsmen to convert good starts into big scores after the aborted first Test in Durban and seemed determined to set an example against steady bowling on a pitch still offering some help to the seam bowlers.
South Africa's total advanced by 154 runs from their overnight total of 283 for three, for the loss of three more wickets in 54 overs.
JP Duminy 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. 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.
Stiaan van Zyl, a late replacement for the injured Dean Elgar, made a labored 35 off 111 before he was caught at a wide slip by Ross Taylor off Neil Wagner.
The left-armed Wagner, born and raised in nearby Pretoria, was New Zealand's most successful bowler, taking four for 76.
New Zealand again were on the wrong side of close leg before wicket decisions, using up both their remaining reviews as they sought to overturn not out decisions against Van Zyl and Vernon Philander.