Having suffered a heavy 7-1 loss to Argentina in their Olympic opener on Sunday, South Africa set out to get their campaign back on track at the Riverbank Arena and raise themselves off the bottom of the pool B standings.
New Zealand, meanwhile, headed into the fixture fresh from a surprise 1-0 victory over old rivals Australia on the opening day to stand them in good stead for the knock-out rounds.
New Zealand stuck up their hands as major medal contenders as they rarely looked troubled in defence and in the middle of the park where they controlled possession throughout.
South Africa were off to a bad start as the Black Sticks scored just two minutes into the game from their first of seven penalty corners (PC) for the half.
Captain Kayla Sharland dispatched a pinpoint pass to the far post, finding Charlotte Harrison unmarked, with Harrison slotting home past South African goalkeeper Mariette Rix after a well-worked PC routine.
New Zealand looked in full control in the opening period, as their impressive defensive unit led from the back, building momentum for their attackers, while easily dealing with any South African attempts at goal.
The Kiwis stretched their lead to two with 20 minutes on the clock through their sixth PC, which Clarissa Eshuis converted expertly into the bottom right corner of Rix's goal, leaving the keeper with no chance.
South African striker Pietie Coetzee - in her 250th international Test - had the best chance of the half for South Africa as she deflected a superb cross from Tarryn Bright at New Zealand goalkeeper Bianca Russel, who had no problem in dealing with the Coetzee's effort.
The Black Sticks were awarded a controversial goal six minutes from the break as Sharland appeared to have scored, before South African skipper Marsia Marescia called for a video referral, claiming the goal was scored from outside the area.
However, the appeal was turned down and New Zealand's third goal stood, leaving the South Africans 3-0 down at the break.
South Africa came out into the second period looking more composed and seemed to settle into their structures better than in the first.
Coetzee continued to be a thorn in the Kiwis' side as she marked her milestone with a goal from a penalty stroke, after Jennifer Wilson was bundled over in the New Zealand area.
With eight minutes to play, New Zealand all but killed the contest when Sharland bagged her second of the match after a good run into her opponents' half, before unleashing a rocket at goal which beat Rix high to her right.
Olympic Games field hockey results on Tuesday:
Women
Belgium 0 China 0
Netherlands 3 Japan 2
Great Britain 5 South Korea 3
Group B
South Africa 1 New Zealand 4
Argentina 0 United States 1