When bad light ended play four overs early on Sunday, New Zealand were 67 without loss in reply to South Africa's 314.
Latham, who managed 24 in total in three previous innings in the series, was unbeaten on 42 after coming out on the right side of two reviews, with Jeet Raval on 25.
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With New Zealand needing to win to square the series, it proved a successful day for Latham who had a standout performance in the field highlighted by an instinctive catch at short leg to remove Faf du Plessis.
But de Kock proved a much tougher obstacle on a frustrating day for the players when only 26 balls were possible between lunch and tea after rain also cost nearly three hours of play the previous day.
Just as his 91 in the first innings in Wellington set up South Africa up for an eight-wicket victory, de Kock again tormented New Zealand with his trouble-free approach.
When he went to the middle with the fall of Temba Bavuma's wicket, South Africa were 148 for five and he held the innings together while the bottom half of the batting order added a further 166.
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De Kock's 90 came off only 118 balls, highlighting why captain Faf du Plessis was determined to have him play despite the wicketkeeper-batsman suffering ligament damage to his right index finger.
He hit 11 fours and two huge sixes, one off New Zealand's best performed bowler Matt Henry and one off Jeetan Patel, as he dominated the off-spinner who had claimed his wicket cheaply in the drawn first Test.
But 10 runs short of his century he played across the line to Neil Wagner and was out lbw.
South Africa resumed the day at 123 for four and after Henry removed Bavuma for 29, du Plessis progressed to 53 before a smart piece of fielding by Latham at short leg.
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On the third ball of Mitch Santner's opening over, Latham anticipated du Plessis was going to sweep and before the shot was played he was moving to his right where he flung out an arm to take the close-range catch.
Latham took another classy catch, just above ground level to his right at second slip to remove Vernon Philander for 11 off Henry.
Henry equalled his career best figures with four for 93, while Neil Wagner, who took three for an expensive 104, ended the South Africa innings with the wicket of the hard-hitting Kagiso Rabada who scored 34 off 31 deliveries.
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