Sydney Morning Herald writer Greg Baum described it as an "exorcism" for the Kiwis after losing six semifinals in the past.
"New Zealand seized the day, South Africa seized up."
He praised Grant Elliott's "memorable triumph" over his former home nation, while captain Brendon McCullum was "New Zealand personified".
"Don't write this off as Eden Park's mini-boundaries; McCullum was clearing them on a scale that Lord of the Rings director Peter Jackson would not dare to script," Baum said.
"The crowd played its appointed part; all day, the South Africans bowled and hit into the teeth of its roar. The Eden Park stands heaved and bellowed as they cannot have since the 2011 rugby World Cup final."
Baum described the Black Caps' 2015 world cup performance as "compelling", and "sweeping up the country, making believers of sceptics and evangelists of believers".
"But always when a good New Zealand cricket team emerges, a sense lingers that like a fable from Middle-earth, it will finish in a moment, and the lights will go up. Not this time; these Kiwis are for real."
The Sydney Telegraph described an "epic semi-final", and praised "Elliott's decisive blow against the country of his birth" to give New Zealand the win.
The newspaper called the game: "One of the greatest World Cup contests in the 40-year history of the tournament."
It also featured a photograph of Elliot consoling South African Dale Steyn as he lay on the ground at Eden Park, calling it the "perfect image of sportsmanship" and the "enduring image of the semi-final".
The ABC described the triumph as a "dramatic win", and said the Black Caps had "played out a World Cup semi-final thriller at Eden Park" against South Africa, with the team "claiming a place in the final with a dramatic penultimate-ball victory".
Meanwhile, some of crickets biggest names took to Twitter to voice their opinion on the win.
South African-born England batsman Kevin Pietersen posted: "South Africa DID NOT CHOKE! They got beaten by a better team today...AB led the team wonderfully well! But, well done NZ! See you in Sydney!"
Australian cricket legend Shane Warne said: "What a game of cricket in NZ, please hold your heads high South Africa, you've done everyone proud as you gave it absolutely everything !!"
Australia cricket coach Darren Lehmann said: "Congrats @NZcricket1 and congrats @BrendonMcCullum and team , loved the ANZAC spirit well done to Grant Elliott !"
Australian Ed Cowan said the game was "as good as sport gets".
"Don't think the SA boys will be sending Mr Duckworth and Lewis a Xmas card anytime soon," he added.
Aussie batsman Aaron Finch simply said: "What an amazing World Cup semi final..."
