The weather curtailed any further play.
New Zealand pace bowler Neil Wagner finished with three wickets for 47, dropping his average below 30 for the first time in 22 tests.
"We were happy to bowl first with the humidity and overcast conditions. We hoped it would swing around a bit," he said. "We bowled in partnerships at the start and did so for long periods. We spoke about creating pressure at both ends and, as a unit, we did that. It looks like a tough wicket to score on.
"With the wicket having more bounce, and a touch quicker than Bulawayo [against Zimbabwe], the margin for error was smaller for bowlers if you got carried away."
Despite four wins in 41 tests, the Black Caps have failed to win any of their 14 series against the Proteas dating back 84 years.
The sides have been evenly matched on occasion.
It was 1-1 going into the final two tests of the five-match series in 1961-62 before South Africa won the fourth at Johannesburg and New Zealand won at Port Elizabeth to draw the series 2-2.
New Zealand took a 1-0 lead into the Boxing Day test at Durban in 1994-95 until the tour became infamous, not only for a cannabis-smoking incident but also because the visitors were the second side in history - and the first in 106 years- to lose a three-test series after being one up.
New Zealand were also ahead after two tests of the three-match series in 2003-04 before South Africa levelled the contest 1-1 at Wellington.
In 2016, the hosts have seldom been more vulnerable in the 25 years since their post-apartheid return. Accomplished players such as Hashim Amla, Steyn, Vern Philander and Faf du Plessis remain, but the absence of AB de Villiers and Morne Morkel offers the visitors an opportunity.
Philander, who obliterated New Zealand with 5-7 in the '45' test victory at Cape Town during January 2013, is playing only his fourth test in 20 months and Steyn has missed six of South Africa's last eight tests with groin and shoulder injuries.
The 33-year-old went into the match having taken 58 wickets at 17.05 in 10 tests against New Zealand and had immediate success tonight.
His pace was down, as he had predicted, but he took advantage of the helpful conditions and had figures of 2-3 from his six-over spell before lunch.