The Proteas took a 31-run first-innings lead when they bowled out the Kiwis for 211 in reply to their 242.
At lunch on Thursday, South Africa were 3-88 with David Bedingham unbeaten on 34 and Zubayr Hamza on 14.
South Africa chose not to have the Seddon Park pitch rolled before the start of play, resulting in some intermittent sharp bounce.
Tall New Zealand seamer Will O'Rourke made use of the conditions to remove Raynard van Tonder (one) and Proteas captain Neil Brand (34) in the first session.
The inconsistent nature of the pitch was reflected in the fact O'Rourke bowled in tandem with left-arm spinner Rachin Ravindra, who was introduced after only nine overs with the new ball.
Ravindra dismissed Clyde Fortuin (three) in his second over, the opener falling to a flighted ball which pitched on leg, turned back and crept under his attempted shot, hitting his back pad in front of middle stump.
O'Rourke began the day on a hat-trick of sorts after taking the last two wickets of South Africa's first innings with consecutive balls.
His extra height and pace allowed him to find more bounce than Tim Southee or Matt Henry, who shared the new ball.
Van Tonder was out trying to hook a short delivery which got up to head height. He was unable to get on top of the bounce and the ball carried to Neil Wagner on the boundary at fine leg.
Brand hit consecutive fours from O'Rourke in the 16th over - a pull through midwicket and a firm push through cover - on his way to his highest total in the series so far.
He made four and three in the opening Test of the series, and 25 in the first innings in Hamilton.
Brand had made 34 of South Africa's total of 39 when he received a superb ball from O'Rourke which nipped back from outside off, took the inside edge and was caught behind by Tom Blundell.
Bedingham and Hamza scored freely in the lead-up to lunch which will concern New Zealand captain Southee as every run is likely to prove precious.
New Zealand would be reluctant to chase more than 250 on the fourth or fifth days on a pitch which is deteriorating.