South Africa's David Bedingham scored a maiden century on Thursday to leave New Zealand with the challenging task of scoring 267 to win the second and final Test in Hamilton.
New Zealand, inspired by debut seamer Will O'Rourke's five-wicket haul, were 40-1 in their second innings at stumps on day three, still 227 short of their target.
Tom Latham was not out on 21 while Devon Conway was trapped leg before wicket by Dane Piedt for 17 in the day's final over.
The highest successful fourth-innings chase by any team at Seddon Park was 212, achieved by Australia against New Zealand 24 years ago.
Support from Petersen
Bedingham's career-high 110 was comfortably the standout knock in South Africa's second innings of 235, supported by 43 from Keegan Petersen and 34 from captain Neil Brand.
It hands the understrength tourists an opportunity to square the series 1-1 and deny the Black Caps their first-ever series win over the Proteas.
With his team 31-runs ahead on the first innings, Bedingham batted aggressively in difficult batting conditions.
The 29-year-old scored 12 fours and two sixes in a 141-ball stay that backed up his 87 from the first Test in Mount Maunganui, which South Africa lost by 281 runs.
Bedingham and Petersen combined for a crucial fifth-wicket stand of 98 before Petersen's dismissal sparked a collapse, with the last six wickets falling for 33 runs.
O'Rourke had too much pace and bounce for the tailenders, finishing with 5-34, giving him nine wickets in an eye-catching Test debut from the 22-year-old.
Earlier, he removed Raynard van Tonder for one and then Brand in quick succession to have South Africa in trouble at 39-3.
Phillips stars for Black Caps
Glenn Phillips, who claimed two wickets with his part-time off-spin, pulled off three catches in the gully, two of them spectacular.
Phillips' easiest catch was to remove Bedingham off an O'Rourke delivery that climbed steeply.
Bedingham was able to capitalise on New Zealand's failure to include a specialist spinner on a pitch that is favouring slow bowlers, scoring freely off Phillips and Rachin Ravindra.
New Zealand's biggest threat in their run chase shapes as offspinner Piedt, who took five wickets in the first innings.
AFP