New Zealand have at least given themselves a sniff in the final match of the season; and for that they can thank their captain Kane Williamson.

In equalling Martin Crowe's record of 17 test centuries, Williamson batted beautifully at Seddon Park today, and also with enough pace to push New Zealand to a slim first innings lead over South Africa by stumps.

They start tomorrow at 321 for four, seven runs to the good.

They have only one course of action from here if they are to square the series; somehow get to 450 or more, then throw everything at the South African batsmen and quietly clasp their hands in supplication that every bounce of the ball goes their way over the next two days.

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Bet on the fact there won't be a declaration from South Africa and why should they. They have a fine away record to enhance.

''Very positive," is how opener Jeet Raval described the mood in the New Zealand dressing room.

''We're in a really good position. Six wickets in hand, if we can get a good lead tomorrow and get early breakthroughs then we're right in the mix and it sets up for a good final day."

Quality seamer Morne Morkel, who celebrated his 250th test wicket today, called it ''a fantastic day of cricket", which produced 254 runs and four wickets in 78 overs.

'There's only one team under pressure and that's us. We need to come with the right attitude tomorrow."

Williamson's third century against South Africa, and second in this series, was a brilliant exhibition of the art of batting. His footwork off back and front foot was expert, he cut adroit, drove and clipped off his legs with precision.

''I felt like a clown batting with the master out there," an admiring Raval said.

Williamson pulled Philander with enormous vigour for six over square leg to become the sixth member into New Zealand's 5000 test run club and repeated the shot to Morne Morkel with almost ferocious intensity.

There were three sixes - a 33 percent increase on his tally before today - and he put the momentum into the innings, his runs coming off 216 balls in 330 minutes. He had the field covered as far as South Africa's attack was concerned.

Raval went about his business differently, stubborn rather than stroke-laden, before falling 12 short of a maiden century to a fine diving one-handed catch by Quinton de Kock off Morkel.

His stand with Williamson, 190, is a record against South Africa for the second wicket, and his resolve deserved a century.

Raval did get bogged down at times - 21 runs in the two-hour middle session - and the Auckland lefthander had to scrap hard.

But that's five half centuries in his seventh test now, and an average of 44.8. He had a life on 82, when Faf du Plessis put down a hard one-handed chance off part timer Dean Elgar, and some awkward moments, but hung in the fight.

The latter part of the day belonged to the South African bowlers as the spotlight fell again on the New Zealand middle order.

As it is so much, once again, rests on Williamson.

If he replicates his performance tomorrow, and gets some decent support, New Zealand might be able to eke out a situation when they might just have a chance. No pressure, then.