The Proteas' fast-paced success, their fifth biggest Test win over New Zealand, was all but secured after they bowled the tourists out for just 45 on the opening morning.
The Black Caps were never likely to recover from slumping to their lowest-ever total against South Africa, and only Dean Brownlie's maiden century stretched the contest beyond halfway stage of the scheduled five days.
Victory ensured South Africa, the top-ranked Test nation, will go an 11th series without defeat before the second and final match in Port Elizabeth begins on January 11.
Seamer Vernon Philander was named man of the match, after he inspired the opening-day demolition with five for seven, although he and his team-mates were at least made to toil by Brownlie in New Zealand's second innings.
The 28-year-old right-hander continued his resistance on Friday morning to reach three figures for the first time. He did so without fear too, clubbing Robin Peterson for a pulled six to go to 98 before dancing down the wicket to the same bowler in his next over to again clear the rope and prompt his celebrations.
With overnight partner BJ Watling content to stonewall, the duo looked set to bat out the morning session only for Brownlie to fall, in reckless style, to the new ball just before lunch.
His dismissal undermined the work he had done beforehand as he slashed at Morne Morkel, picking out Peterson on the rope, after he had reached 109.
New Zealand's tail then quickly followed after lunch as the Proteas eventually completed the job by dismissing the visitors for 275.
The match ended in some farce as Chris Martin was needlessly run out, following Dale Steyn's throw from the deep, for the 36th duck of his 71-Test career.
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