Hayward claimed a hattrick of goals, his second at a World Cup, as the Kiwis absorbed some pressure from the opening whistle before going about their business with a modicum of dexterity that justified the gulf between their world No6 standing and the South Africans who are ranked No12.
The New Zealanders were clinical from set-piece play with Hayward hitting the backboard from three penalty-corner drag flicks.
The Black Sticks men have registered two wins from as many games and are perched on the top rung of the ladder on six points in pool B on a superior goal differential.
TV commentators likened the game to the traditional rugby rivalry between the All Blacks and the Springboks and it lived up to its billing at times, albeit not in result.
The defenders upped the tempo on the foundation of physicality with one umpire warning Dylan Swanepoel to "cut it out" as he tried to stifle Hayward in the attacking third.
South Africa arguably had two chances to score but they were often guilty of trying to go aerial too often and failing to exploit the space down the flanks in a bid to work the ball into the business sector.
In the few times they got into the danger zone, they seemed bereft of ideas and coughed up possession too easily.
"Any time teams from the top 12 in the world are involved it's a tough battle. South Africa have always been tough and really close so we have to break them down," McAleese said, thankful Hayward was in fine form to ease the pressure.
It was imperative, he said, for players to try to figure out how much license umpires were going to give players at the World Cup.
Conversely players also were keen to push the boundaries on each other to bring green and yellow cards into play for territorial advantage.
"So it's pretty much a test of what you can or can't get away with. We don't want to do anything that'll cost us a goal, a card or result in a stupid foul," he said.
The Black Sticks men now play Argentina tomorrow at 11pm (live on Sky Sport 1), after the latter hung on to upset Olympic champions Germany 1-0. The Netherlands pipped South Korea 2-1 yesterday.
The Kiwis then play the Germans and the Dutch before the playoffs.
"The Argies bring a lot of passion and determination so it'll be one hell of a match."
Result: Black Sticks 5 (Andy Hayward 3, Simon Child, Shea McAleese) South Africa 0.
Halftime: Black Sticks 3-0