Tahir, who was on a hat-trick in his second over, had his figures ruined by successive sixes from Colin de Grandhomme but still finished with 5-24 in 3.5 overs, with the Kiwis unable to pick his googly.The 37-year-old did reap the benefits of a superb bowling performance by the rest of the team with Chris Morris, who was also denied a hat-trick, having figures of 2-10 in his opening three-over spell.
Andile Phehlukwayo took three wickets, including the important wicket of New Zealand captain Kane Williamson, as the hosts crumbled to 107 in 14.5 overs while chasing South Africa's 185-6.
The loss was New Zealand's first at home this summer.
Both sides had said beforehand they felt just having one Twenty20 clash before the five-match one-day series did not have much meaning and more games should have been scheduled.
The South African top order, however, underlined how dangerous they would be in the one-day series with nearly all making telling contributions.
While Quinton de Kock fell for a duck in the third over, Hashim Amla (62), captain Faf du Plessis (36), AB de Villiers (26) and JP Duminy (29) all scored quickly.Amla's innings was particularly impressive as he played just pure cricket shots to hit nine boundaries and a six in his 43-ball innings.
The opener also combined with du Plessis in an 87-run partnership from 8.3 overs and the visitors looked well set to score in excess of 200 if the pair could stay at the crease.
De Grandhomme, however, dismissed both du Plessis and de Villiers to leave their side on 145-4 in the 16th over ensuring the all-rounders needed to push the innings on.Opening bowler Trent Boult finished with an impressive 2-8 from four overs.The first one-day international is at Seddon Park in Hamilton on Sunday.