New Zealand held an eight-goal lead in the first quarter, before South Africa came roaring back to lead late in the fourth quarter, as they looked set for just their second win over the Ferns in 33 matches.
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But Silver Ferns shooter Amerliaranne Ekanasio showed nerves of steel, as she hit a clutch shot to send the match into extra time.
After two seven-minute periods, the scores were locked at 57-57, so the match would keep going until one team held a two-goal buffer.
Noeline Taurua's side held their nerve, as Maria Folau landed the game-winning shot that saw New Zealand finish third on the standings, behind England and Australia.
The win means the Silver Ferns avoid finishing the Quad Series without a victory for the first time.
New Zealand got off to a fantastic start, as they scored the first eight goals of the game, before South Africa got on the board, as they raced out to a 14-9 lead at the end of the first quarter.
Errors started creeping into the Ferns' game, as the Proteas continued to close the gap in the second, outscoring New Zealand 11-8 in the quarter to trail 22-20 at the break.
By the end of the third, the match was all square at 34-34 and South Africa took the lead for the first time in the early exchanges of the final quarter, as poor decision-making continued to cripple the Ferns.
With the scored tied at 44-44 in the final minute, Lenize Potgieter put South Africa in front, before Ekanasio's long-range shot sent the match into extra time.
South Africa took a two-goal lead early in the first period of extra time and New Zealand had to claw their way back, capitalising on mistakes from the Proteas to level things up and extend the match.
Eventually, after 20 minutes of extra time, the Silver Ferns got over the line, as Folau scored three consecutive goals to secure victory for New Zealand.
Folau finished with 36 from 42 attempts, while Ekenasio was successful with 21 of her 28 shots.
The win was a great way to end the Quad Series, after defeats to host England last Monday, and Australia on Sunday.
England beat Australia 52-49 in their match, but the Diamonds finished on top of the Quad Series standings on goal difference.