Second century for Williamson as New Zealand extend lead past 500

Kane Williamson crafted his second century of the match Tuesday as New Zealand took complete command of the first Test on day three against understrength South Africa.

Run machine Williamson was out for a rapid 109 as the home side reached 179-4 in their second innings at Mount Maunganui, extending their overall lead to 528 runs by stumps.

Daryl Mitchell was at the crease on 11 and Tom Blundell on five, with the Black Caps looking to declare early on Wednesday with South Africa facing a mammoth target on a deteriorating Bay Oval pitch.

The depleted Proteas were dismissed for 162 soon before tea in response to New Zealand's first innings 511.

The follow-on wasn't enforced, allowing the world's top-ranked batsman Williamson to craft another big score to follow his 118 in the first innings.

It was the former skipper's 31st Test century but the first time he has reached three figures twice in the same match.

The 34-year-old played with aggression from the outset, striking 12 fours and a six in a 132-ball stay that signalled New Zealand's intent before he was stumped off the bowling of Proteas captain Neil Brand.

As was the case in the first innings, Williamson survived a dropped catch in the outfield, with Edward Moore again the culprit when he was on 61.

Moore responded in the following over by catching Devon Conway for 29 off captain Neil Brand's bowling, ending a partnership of 92 with Williamson after opener Tom Latham fell cheaply.

First innings double-centurion Rachin Ravindra departed soon afterwards for 12, caught off the spin bowling of Brand, who took six wickets in the first innings.

The second-string nature of South Africa's side was exposed when they lost their last six wickets for 82 runs on Tuesday.

The top score was 45 from Keegan Petersen who, in his 13th Test, is the most experienced batsman in the squad after most first-choice players remained behind to compete in a domestic Twenty20 competition.

New Zealand's Mitchell Santner takes a catch to dismiss South Africa's David Bedingham. By MICHAEL BRADLEY (AFP)

Petersen lost his overnight partner David Bedingham for 32 when trying to hook seamer Matt Henry, before Ruan de Swardt followed for a second-ball duck in the same over.

Wicketkeeper Clyde Fortuin, one of six Proteas debutants, departed for nine just before the tourists went to lunch at 129-7.

The tail was wrapped up quickly, with Henry taking 3-31 and Mitchell Santner capitalising on spin-friendly conditions to finish with 3-34.