Nicholls and Wagner put on 80 for the fourth wicket to put the hosts into a strong position at 4-235, after dismissing South Africa for 95 on the opening day in Christchurch.
Nicholls is undefeated on 86 while Daryl Mitchell is 14 not out.
New Zealand resumed at 3-116 Friday, a lead of 21 with Nicholls 37 not out and Wagner on two. Wagner immediately went on the offensive, hitting a series of boundaries which shook the confidence of the South African bowlers.
He first took on Kagiso Rabada, swinging hard when given width and taking a series of boundaries behind point. He also advanced when the ball was fuller and hit sweetly down the ground, at one point leaning into a textbook cover drive.
Wagner hit seven fours and two sixes, the first of which came from a streaky top edge but the second of which was a classy flick over the head of square leg.
Nicholls was watchful, leaving as often as he was able to and reached his half century from 80 balls. With the momentum generated by Wagner, New Zealand added 74 runs from 14 overs in the first hour.
The South African bowlers showed signs of frustration. Rabada, Glenton Stuurman, Marco Jansen and Duanne Olivier were all put off their lengths by Wagner's onslaught and struggled to produce the concerted bowling effort that was necessary as New Zealand's lead mounted.
Wagner was out three balls after the drinks, on the brink of his second Test half century. He flicked a ball from Rabada off his pads but managed only to pick out the fielder at square leg, letting out a yelp of frustration.
Nicholls is batting one place higher in the New Zealand order than usual, in the absence of captain Kane Williamson who has an elbow injury.
He played a vital role on the first day, putting on 75 for the third wicket with Devon Conway (36) as New Zealand attempted to capitalise on their outstanding bowling effort.
Seamer Matt Henry took 7-23 as New Zealand bowled out South Africa cheaply after winning the toss.
