Tahir and fellow bowlers Kagiso Rabada (three for 25 from 7.1 overs), Andile Phehlukwayo (two for 35 from seven overs) and Chris Morris (one for 34 from nine overs) worked in partnerships to ensure no miraculous Black Caps escape.
"It was amazing, he [Tahir] likes bowling here," South African captain AB de Villiers said. "He gets bounce and things happen quicker. He had rhythm and controlled the game well for us, drying it up from one end.
Given South Africa had lost the World Cup semi-final to New Zealand at the same venue, de Villiers was taking nothing for granted.
"We created great pressure, but I was never at ease as captain. I felt anything over 200 would be difficult to chase in 'a final'. Once we got the sniff, I felt it was important for us to chase it down and finish it off.
"I had 150 in mind as a restricted total early, once we got [Kane] Williamson, [Ross] Taylor and [Martin] Guptill. But I knew if [Mitchell] Santner and [Colin] de Grandhomme had batted 10 or 15 overs, we could be in trouble."
"There's a bit of emotion in us winning the series. We'll enjoy the victory. It doesn't make it right after we lost the semi - that will never change - but as we sit here now, we've just won a game against New Zealand in 'a final' at Eden Park so it's a great feeling. We've come a long way since that semi-final."
"It was tough to rotate the strike out there," New Zealand captain Kane Williamson said. "When you are under pressure and lose wickets, that is something you look to do to bring momentum back, and that wasn't happening.
"We lost a number of wickets around Imran which made it difficult. We needed two guys to stick there for a 'death phase' so we had wickets in hand to go harder."