De Grandhomme was the last wicket to fall, just on tea, in a Test New Zealand need to win to square the series.
After resuming the day seven runs ahead, New Zealand consolidated their lead with 76 runs in the morning session before de Grandhomme picked up the pace to put New Zealand in a strong position.
His 57 came off 70 deliveries and included five fours and two sixes.
With South Africa on the back foot, de Grandhomme and BJ Watling chased the runs after lunch, adding 46 in 13 overs.
But Watling played on to Keshav Maharaj and was gone for 24.
Matt Henry added 12 and Jeetan Patel five before the innings folded with de Grandhomme gloving a Morne Morkel flyer through to wicketkeeper Quinton de Kock.
It was de Kock's fifth catch of the innings and third off the bowling of Morkel.
He faced 285 deliveries in a marathon innings which lasted more than seven hours and included 16 fours and three sixes.
In the last over before lunch, Santner nicked Kagiso Rabada to JP Duminy at gully to be gone for 41.
Ahead of taking the third new ball, South African skipper Faf du Plessis looked to buy a wicket by calling on Temba Bavuma. He had only bowled twice before which included the wicket of Josh Hazlewood in Australia four months ago.
Morkel finished with four for 100 and Rabada took four for 122.
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