South Africa were 63 for three at lunch on Monday, an overall lead of 12.
The home side were in early trouble when captain Graeme Smith's dismal run of form continued.
He was trapped in front of his stumps by Chris Martin for seven in the third over of the day when just four runs had been added to South Africa's overnight total of four for no wicket.
Smith's opening partner, fellow struggler Herschelle Gibbs, failed for the second time in the match when he was caught at second slip off James Franklin for two.
First innings top scorer Boeta Dippenaar started promisingly but when he was on 16 he got a ball from Jacob Oram which kicked and he edged a low catch to New Zealand captain Stephen Fleming at first slip.
As on the second day, the ball deviated alarmingly at times during the morning period, with play starting at the unusually early hour of 9.30 to take account of the early sunsets of South Africa's autumn.
Jacques Kallis and Ashwell Prince both had awkward moments but were able to survive until lunch in the hope that conditions would ease during the afternoon, as happened Sunday.
Seven wickets fell before lunch Sunday but New Zealand recovered from 45 for five to score 327, a lead of 51, largely through a seventh wicket stand of 183 between Oram (133) and Daniel Vettori (81).