Cape Town, January 2013. New Zealand are decked for 45 in the first innings of a Test. Vernon Philander has five wickets. Dale Steyn and Morne Morkel the other five. New Zealand's second innings is a little better. Their second Test is not. Through this disastrous series there is a string of meetings. Which way forward? How to overcome this almighty rut?

"We knew we had to make changes - for the public who cared about this team," Brendon McCullum has said of that time. "It was essential to all of us that we have the public's support. The best way to get that is to go out and represent New Zealand with all you've got."

On Tuesday, the greatest stadium in the country became a living, breathing, 41,000-strong cardiogram for their national cricket team. Their cries lived out Trent Boult's first, sniping spell. The ball would rush by Quinton de Kock's blade and hands would rush to heads all over the South stand. The slips' oohs and aahs were mouthed on both tiers, in the uncovered seating beyond deep cover. This was no ordinary home support. This was all-consuming love. This was hard-earned respect. It was the apex of New Zealand's World Cup, and Eden Park would let the world know it.

Luke Ronchi made New Zealand's first mistake. With an outswinger that went late, at almost yorker length, Trent Boult drew de Kock's outside edge, but the keeper spilled the chance, diving hard and low to his right. The bowler kept it together, but men and women in the stands could not. There were frustrated slaps on thighs. Gritted teeth and swearing, followed by applause to raise spirits again. Boult was so skilful early, another chance would surely come.

The first three wickets were met with deafening roars, but when Kane Williamson dropped AB de Villiers at cover, he was swiftly forgiven. This is a crowd that has formed bonds to fit each player. They have seen Williamson pull off screamers at gully, so they know the drop was not for want of effort or dedication.

When old man Daniel Vettori, he of the climbing one-handed grab from the last match, chased balls and reeled them in near the boundary, he was given full-blown standing ovations. He is the man who was once the blond-haired tyro at 18, then New Zealand's talismanic captain through one of their bleakest periods. His name has been on the nation's lips the longest, and it came easy to this crowd when he took the ball at the end of his busy run-up. He would take no wickets in his nine overs, but all through, rhythmic chants of "Da-niel Ve-ttori" rang out. Every time he touched the ball, another cheer.

Like the team, Eden Park was quietened by David Miller and AB de Villiers' late charge, but when McCullum was flaying one of the greatest quicks of the 21st century for 25 in an over, the whole stadium's confidence rose to match his arrogance. McCullum's 32 minutes at the crease brought for the first time a grimaced clenching of fists and a snarling intensity. The batsman's manic bat-speed and rippling muscle had seemingly delivered assurance. Then he got out. Silence.

Through the middle overs the crowd and their team lived on a precipice. Every New Zealand advance, no matter how minuscule, was celebrated. Singles were cheered like hundreds, and even South Africa's field changes were booed. New Zealand is a laidback country. Its people are usually measured and reasonable. But here, tens of thousands of them had become fanatics.

As wickets were lost and the finish approached, nerves began to fray. Twice Elliott hit balls high in the air. Once it dropped safe, in the pinpoint middle of three converging fielders. The other time, it slipped through deep square leg's hands, as fine leg almost crashed into him. You heard the whole stadium exhale. Restless-leg syndrome swept through like a pandemic. Vettori's last-over four through third man brought a curt welling of noisy hope. Then there was quiet as the ball left Steyn's fingertips, fizzed through the air, pitched, and hit Elliott's bat, but when the trajectory was certain, the noise was something else. Surely nothing louder has been heard on planet earth today. Friends were high-fiving, strangers were hugging. They were all going to the final.

It wasn't so long ago that this New Zealand team were pariahs at home: whitewashed by Bangladesh, five lost Tests in a row. It wasn't so long ago Tim Southee spat abuse at batsmen even when he had been smeared around the ground, or Brendon McCullum said on national radio: "We stopped listening to Martin Crowe years ago," when New Zealand's greatest batsman had simply suggested McCullum play in a different position.

But even before this long, glorious home summer, New Zealand's public had seen change. This was not the same team that Stephen Fleming led on a verbal warpath against South Africa in 2003. This was the side that was so bruised by Phillip Hughes' death they did not bounce their opposition for a whole day of the Sharjah Test last year. This was a team so respectful of greatness that to a man they congratulated Kumar Sangakkara after his Basin Reserve double-hundred, and later described that innings as an educational experience.

It has all been said over and over this tournament: "McCullum is a dreamy captain", "New Zealand attack without relent", "They play like they have nothing to lose." But never let it be forgotten they won hearts as well as matches. Don't let it be forgotten they have stirred a nation with their humility, their unflinching devotion, their bloody-minded approach. Whatever happens in Melbourne on Sunday, whichever cricket giant they wind up playing, New Zealand were adored by their public on this electric night.

Through their fans, New Zealand have found a way forward. They have overcome the rut.