A 190-run record second-wicket stand between Kane Williamson and Jeet Raval saw New Zealand wrest control back against South Africa on the third day of the third test in Hamilton.

The Black Caps reached 321 for four in reply to the Proteas' 314.

Williamson's unbeaten 148, and a test best 88 from Jeet Raval demoralised the visitors for most of the day. Their partnership eclipsed the 102-run record they posted for the same wicket in the first test at Dunedin.

The batting was of low risk and maximum impact, the type expected from New Zealand sides, particularly at home. The result was a palpable improvement on the side's ineffective second innings at Wellington. They made South Africa look flat in the field. Despite accurate lines, bouncing the ball on the block strips to enhance its reversing qualities, and intense pow-wows between captain Faf du Plessis and his bowlers, the visitors' attack struggled to penetrate.

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Williamson reached his 17th test century equalling Martin Crowe's New Zealand record.

He also became the sixth Kiwi to reach 5000 test runs when he pulled Vern Philander for six over square leg.

Among New Zealand batsmen, only Stephen Fleming (7172 runs), Brendon McCullum (6453), Ross Taylor (6030), Crowe (5444) and John Wright (5334) had passed that mark before today.

Williamson is the fastest in 110 innings, seven inside Crowe's old mark. At 26 years and 231 days he is the third youngest test player to complete the feat behind Sachin Tendulkar and Alastair Cook.

None of that will infiltrate the captain's mindset as he strode through the pickets at stumps. The match result is the sole barometer for cricket's patron saint of modesty. An example was when he was offered the light by the umpires at 6.47pm; Williamson decided to continue, thus maximising the chance to score runs, and advance the match. Mitchell Santner was unbeaten with him on 13.

Williamson unfurled back foot punches through cover point, drives either side of the wicket and late cuts, all with footwork that would receive unanimous 10s on Dancing With The Stars.

After Tom Latham edged Morne Morkel behind for 50 off 103 balls - the pace bowler's 250th test wicket - the New Zealand captain extended local fortunes.

He made his lowest test aggregate (3) at Wellington, but shrugged off that cloak of disappointment the moment he leant into a cover drive off Morkel to go from two to six. From there he was a picture of batting application. His influence was further bolstered by a rare test six - the 10th of his career - on-driving Keshav Maharaj towards the sightscreen and holding the pose. Two further maximums were pulled from Philander and Morkel.

Raval continued his fine debut summer as opener with a fifth half-century from 12 innings. He was strong off his legs behind square and executed several controlled (and the odd uncontrolled) guides through the slip cordon. Only 27 of his runs came in front of the wicket, evidence he was committed to the leave and seldom tempted by the South African lines.

It's one of cricket's drollest observations that there are two types of leave "good ones" and "bad ones". Raval completed a "good one" by a coat of paint to Morkel in the 50th over as the ball zoomed back past the stumps from outside off.

Latham boosted his confidence after a lean spell of form. He glanced Morkel to fine leg to post his 13th half-century after starting the day at 42. Wickets were scarce for South Africa, so wicketkeeper Quinton de Kock throwing out a left glove in a one-handed take as he dived towards first slip was brief respite. It didn't affected his dodgy right index finger. His switch of direction to dive and remove Raval from an inside edge might have, but he didn't flinch.

Raval and Latham put on 83, just the third New Zealand opening partnership to muster more than 50 against South Africa in 38 attempts this century. Williamson benefited from what was effectively a padded-up vacation, given the previous highest opening stand for either side this series was 18.

Neil Broom (12) and Henry Nicholls (0) fell to consecutive Kagiso Rabada deliveries with the score at 293, but the day had long become New Zealand's.

Play started at midday under a blue and grey quilted sky, but overnight rain saw the ground staff earn their keep all morning, including a spell under lights. The umpires declared the ground fit for play at midday following an 11.15am inspection.