Proteas fast bowler Kagiso Rabada reduced New Zealand to 157 for five on day two of the second Test at the Hagley Oval in Christchurch on Saturday.
Rabada had openers Tom Latham and Will Young caught by wicketkeeper Kyle Verreynne before bowling middle-order batsman Tom Blundell.
Verreynne snared a diving catch down the leg-side to remove Latham – and later did the same off the bowling of seamer Marco Jansen to dismiss batsman Devon Conway.
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New Zealand trailed by 207 runs at the close of play, after all-rounder Colin de Grandhomme counterattacked with an unbeaten half-century.
“Tomorrow we’re just going to go hard, try to make them play as much as possible and try to force them to make a mistake because it is quite a good batting wicket,” said Jansen.
“The plan for tomorrow is just to be as tight as possible.”
South Africa had collected 364 all out in the first innings. Opener Sarel Erwee struck a century.
This marks an improved performance from the tourists, who slipped to heavy defeat inside three days in the first Test at the same venue.
South Africa made three changes to the XI for this match. All-rounder Wiaan Mulder, fast bowler Lutho Sipamla and Keshav Maharaj were selected.
Seamer Glenton Stuurman, fast bowler Duanne Olivier and batsman Zubayr Hamza were dropped.
They are without fast bowlers Anrich Nortje and Lungi Ngidi, who have been sidelined by injury. Batsman Keegan Petersen is also absent.