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.
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.