Their inability to pick Tahir's googly caused the home batsmen huge problems at Eden Park and their bamboozlement led directly to three of the five wickets he claimed.
With each victim, the 37-year-old embarked on a manic sprint towards the small groups of flag-waving South African fans in the stands.
"He's a big reason why we've had the success we have had in the last 10 months," South Africa captain Faf du Plessis told reporters.
"He's just become so consistent and that's a massive weapon. Even if teams do get off to a good start, you know the chances of him coming on and doing well is very high."
Tahir's man-of-the-match performance, however, was helped by the pressure imposed by opening bowler Craig Morris, who took two wickets in two deliveries, and Andile Phehlukwayo's three wicket haul through the middle order.
"Everyone bowled really well," du Plessis added of the bowling group that did the job without the rested Kagiso Rabada and injured Dale Steyn.
"Obviously the star is Imran but the seamers on that pitch were really good in the areas they bowled."
South Africa's specialist batsmen also dominated New Zealand's bowlers - the exception being Trent Boult (2-8) - with the aggressive David Miller expected to bolster the lineup after he recovers from a cut finger.
New Zealand coach Mike Hesson recognised his side would need to step up in the first of five ODIs on Sunday, when Neil Broom and Ross Taylor return to potentially bring some middle order stability in Hamilton.
"All in all not a great performance and certainly one we're going to have to turn around pretty quickly," Hesson told reporters on Saturday.
"It certainly showed us how many good players they have.
"It was a thorough performance from South Africa but disappointing from our perspective that we didn't fire too many shots at them."
(Reporting by Greg Stutchbury in Napier; Editing by Nick Mulvenney)
