Alviro Petersen moved to 86 not out with JP Duminy on 66 in an unbroken 116-run stand for the third wicket.
Saturday's morning session was again washed out and further rain was forecast for later in the day as the tourists targeted a large total with the aim of bowlingNew Zealandout twice in the abbreviated Test.
Only 42 overs were possible on the first day because of rain in the morning and bad light in the afternoon.
Although the conditions inWellingtonfavour the quick bowlers,New Zealandhave been unable to capitalise on the few chances offered by the sturdy Petersen and Duminy.
The only bad news forSouth Africawas the likelihood they have lost key batsman Hashim Amla for the rest of the match after undergoing emergency surgery on his groin area.
Amla was hit on the first day by an inside edge from a Chris Martin delivery.
He was able to bat on and progressed from 33 to 63 before he was dismissed and then rushed to hospital.
"Hashim underwent emergency exploratory surgery resulting from blunt trauma sustained to his groin region," team manager Mohammed Moosajee said in a statement.
"He spent the night in hospital and was discharged this morning. The surgeon is satisfied with the outcome and expects Hashim to make a full recovery.
"However, it is unlikely that he will be able to take further part in the current Test match at the Basin Reserve."South Africa, who have a 1-0 lead in the three-match series, are without star all-rounder Jacques Kallis for this Test after he was ruled with a stiff neck.