Gerald Coetzee And simon harmer took three wickets apiece as West Indies wavered in their pursuit of an unlikely 391 goal.
West Indies were eliminated for 106. South Africa won the two-game World Test Championship series 2-0.
The teams will now play a three-game ODI series starting in East London on Thursday, which will be followed by three Twenty20 International games.
The match was more or less decided in 8.1 overs before lunch when West Indies reduced to 34 for six.
Fast bowler Kagiso Rabada struck twice in three-ball and sparked the collapse after open batsmen Kraigg Brathwaite and Tagenarine Chanderpaul survived the first 10 overs, scoring 21 runs.
Rabada fired Brathwaite for the seventh time in successive innings when he trapped the West Indian captain’s leg before the wicket for 18 with a ball that went low.
Two balls later, Raymon Reifer gloved a hold on the side of the leg to wicketkeeper Heinrich Klaasen.
Spinners Simon Harmer and Keshav Maharaj also took two wickets apiece as West Indies lost six wickets for 13 runs.
Off-spinner Harmer shared new ball with Rabada and extracted an outlandish turn, catching Chanderpaul on second slip after the southpaw faced 36 balls and scored just two runs.
Roston Chase, Jermaine Blackwood and Kyle Mayers all fell short with South Africa’s only backhand after Maharaj won a successful call for the leg before the wicket against Mayers in the final over before lunch.
In celebration, the left arm spinner collapsed and was stretched off the field with a tendon injury in his left ankle.
Maharaj was taken for a CT scan. With the versatile Wiaan Mulder suffering from a right index finger injury, which also required a CT scan, South Africa were down to just three front row bowlers. The Staff of the West Indies, however, had already been destroyed.
Mulder returned after lunch but was not required to go bowling.
Joshua Da Silva, Jason Holder and Alzarri Joseph all played aggressive shots after lunch as the last four wickets gave 72 runs before the end of the game shortly after the afternoon break.
There had been concerns over Rabada’s fitness after suffering back pain in the opening rounds, but he showed no signs of discomfort during a hostile seven-year spell.
South Africa were knocked out for 321 earlier, with captain Temba Bavuma adding just a single point to their 171 overnight before being caught at Holder’s deep square leg.
(With contributions from AFP)
