Esterhuizen struck 75 from just 33 balls, that included five fours and six sixes, as the Proteas posted a total of 187-4 in their 20 overs after being sent in to bat at the toss.
There were solid contributions from the rest of the of the batters with Rubin Hermann striking 39 while Wiaan Mulder scored 31 in his new role as an opener in the shortest format.
The Proteas innings was given a boost late on when Dian Forrester struck an unbeaten 21 off just 13 deliveries as the visitors got close to the 190-run mark.
The South African bowlers then put in a disciplined performance with ball as the Black Caps were restricted to 154-8.
Gerald Coetzee looked in his best form with the fast bowler returning figures of 2-21 in his four overs.
Ottneil Baartman continued to show he is a best in the shortest format with 2-33 while Mulder also chipped in with two wickets.
Both teams would have taken plenty of positives from the five-match series with most of their first-choice players missing.
Proteas coach Shukri Conrad says the "jury is out" on whether the T20I series in New Zealand should have been given international status but insists the tour has been an "invaluable exercise".
The Proteas levelled the five-match T20I series against New Zealand in Wellington on Sunday, securing a tense 19-run victory in the fourth match to set up a decisive final clash in Christchurch on Wednesday.
New Zealand comfortably secured an eight-wicket win over a weakened South African side at Eden Park in Auckland on Friday, taking a 2-1 lead in the five-match Twenty20 International series.
South Africa's batting coach Ashwell Prince said his team "didn't get any rhythm" after the Proteas were bowled out for 107 in a seven-wicket defeat to New Zealand in Hamilton, leveling the T20 series 1-1.
