The match had been delicately poised entering the final day with South Africa 224 for six in the second innings, a lead of 191 runs, with captain Faf du Plessis on 56 and Vernon Philander on one at University Oval.
Heavy rain that began early on Sunday, however, ensured a delayed start and after the scheduled lunch break was taken at 1 p.m. (0000 GMT), umpires Kumar Dharmasena and Bruce Oxenford decided there was no chance of any play.
"I think the game was shaping up quite nicely for all three results," New Zealand captain Kane Williamson said. "The game was certainly in the balance and it's just a shame not to get any play today.
"But it's nice going into the second match with both teams having played some good cricket."
New Zealand will enter the second match at Wellington's Basin Reserve without batting stalwart Ross Taylor, who tore his calf muscle during the first innings, while left arm pace bowler Trent Boult is under an injury cloud.
"It's a real shame to lose Ross, our premier batter, but therein lies an opportunity for someone else," Williamson added.
"(Trent) does have a little niggle but we don't know how serious it is yet. He will travel with us to Wellington and hopefully he will recover. He is a big player for us."
Du Plessis felt his side could also have won the game had they set New Zealand a target of about 250 runs in 60 overs.
"It was set up to be a great finish," du Plessis said. "We were looking to get about another 50 or 60 runs and on this wicket the ball is turning nicely and (left-arm spinner) Keshav (Maharaj) got five in the first innings.
"The nature of the wicket was you could either get wickets quickly or it's slow scoring and we were favouring our chances because Ross was not going to bat and Trent was injured."
South Africa's opening batsman Dean Elgar, who scored 140 in the first innings and 89 in the second, was named man of the match.
The second game in Wellington starts on March 16, before the third match at Seddon Park in Hamilton begins on March 25.
(Reporting by Greg Stutchbury; Editing by Peter Rutherford)
