At 1pm on Friday, South Africa were at risk of losing a Test. By 7pm on Saturday, they had won it. It took them just 30 hours to turn things around and they did it the full 360 degrees.

"It's happened a few times this season where we've been in impossible situations and then there's one or two guys putting their hand up and making the impossible very possible," Faf du Plessis said. "Lunch time yesterday felt like not too long ago, and now we've won a Test match so just that shift in pressure was really well handled."

South Africa were 104 for 6 at lunch on day two, with Temba Bavuma and Quinton de Kock, the last two recognised batsmen, at the crease. In a stand of 160, they took the score over 250 and put South Africa in the lead. Their fightback was underlined by self-assured batting that, even in the trickiest of situations, they stuck with. Bavuma was cautious and rode the bounce, while de Kock was aggressive. Together, they scored at a rate of 4.13 to give South Africa the advantage.

"We've found this ability to have a lot of faith in our batting line-up, whoever they are, to stand up to pressure situations. Quinton and Temba hadn't been in massive run-spells these last couple of games, so for both of them to do it at a critical time says a lot about them mentally," du Plessis said. "And it was the way they played [that was impressive]. To counter-punch and put the pressure on the opposition was remarkable."

An obdurate last-wicket stand of 57 tipped South Africa over 350 and gave them a match-winning lead, but they did not expect things to come so quickly on the third day. With the southerly wind slicing through the city, South Africa expected being on the field to be uncomfortable at best, impossible at worst.

"It was a challenge for us. What we asked for this morning was real hard cricketers. Mentally we needed to be very strong, to be ready to be challenged and pushed to extremes because it's not conditions we are used to. There were no excuses; the wind and the cold were never going to be excuses. Just real, hard Test cricket and that's what they produced."

The seamers were rotated in short spells and they all seemed to find their rhythms unaffected. Vernon Philander was unlucky not to be rewarded for a probing effort and Kagiso Rabada had his pace up to the mid 140s again, but it was Morne Morkel's new-ball spell that broke New Zealand. He removed both Tom Latham and Kane Williamson, the man South Africa see as "a big threat in terms of holding that batting unit together," as du Plessis has consistently explained. "To get him cheaply obviously helps. We knew if we could get a few early ones we could really put them under pressure."

Morkel then had a third, Neil Broom. He completed a comeback that should see him retained as a certainty in the starting XI for the tour of England in July-August.

"It was a bit of a punt as he's been away from the game for so long. But I knew what I saw from him. Every time he's bowling, he's getting better. In the second innings he hardly bowled a bad ball. His consistency is there and he's getting his pace back up. Today with the new ball, [he] was as tough as you could face. I was standing in the slips and it looked nasty. A lot of bounce with good intensity and pace. When he's on like that, he's a real handful," du Plessis said.

By the time Morkel was done with New Zealand, he had opened them up for Keshav Maharaj, who surpassed all expectations with a second five-for in as many matches.

"It is surprising given the conditions - cold and not a lot of spin," du Plessis said. "But I thought both spinners bowled incredibly well. Their control and consistency meant the New Zealand batsmen just couldn't get away. Their run rates were very low. The pressure that created chances for wickets. When spinners are contributing like that, it makes the seamers' lives much easier, especially with us having to rotate the seamers quite often because we only have three."

The other spinner was JP Duminy, whose low returns with the bat were masked by the career-best 4 for 47 he took in the first innings. Du Plessis still thinks Duminy has an important part to play in South Africa's Test side, with both bat and ball, and hopes Hamilton will be the place where he proves that.

"What was really good for me was the way JP bowled in this match," du Plessis said. "That confidence from the bowling was something I was looking for. We gave him a little bit more responsibility and he got through it really well. He didn't score a hundred in the second innings but the way he played looked really good. It's the way he plays at his best with positive body language."

Firdose Moonda is ESPNcricinfo's South Africa correspondent