After being asked to bat first, opener Hashim Amla (62) struck a quick-fire half-century besides sharing a crucial 87-run stand with first drop and skipper Faf du Plessis for the second wicket.
AB de Villiers and JP Duminy also contributed 26 and 29, respectively to guide their side post a competitive total of 185-6.
In reply, New Zealand were bundled out for 107 runs, with Tom Bruce (33) scoring the highest runs for the hosts.
Tahir was the pick of the bowlers for South Africa as he finished with the figures of five for 24 followed by Andile Phehlukwayo's three for 19.
Chris Morris also bagged two wickets for his side.
Tahir, who also became the second-fastest bowler to take 50 wickets in T20 Internationals, was declared `Man of the Match` for his brilliant spell.
The two sides will now head into five-match ODI series beginning Sunday at Seddon Park, Hamilton. (ANI)