Match referee Javagal Srinath imposed the sanction after Faf du Plessis' side were ruled to be two overs short of their target when time allowances were taken into consideration.
Du Plessis was fined 40 per cent of his match fee for the poor timekeeping, while his players received 20 per cent fines.
As per ICC rules, Du Plessis faces a one-match ban if he is found guilty of one more minor over-rate offence in T20 internationals over the next 12 months.
Dale Steyn was the hero as South Africa claimed a thrilling two-run win, bowling an outstanding late spell as he claimed match figures of 4-17 from his four overs as the Proteas edged to victory.
New Zealand were themselves fined for a slow over-rate on Monday, after falling short of their target in the group clash against England.
