Dale Steyn pocketed 6-34 to claim his 25th five-wicket haul in Test cricket as the Proteas bowled out the tourists, who were 76-2 overnight, for 131 inside 43 overs.
Morne Morkel was the only other bowler to take a Saturday wicket for the hosts, who will look to inflict more misery on their opponents when the second Test begins in Port Elizabeth on Boxing Day.
Leon Johnson and Marlon Samuels headed to the crease for West Indies on the morning of day four, with openers Kraigg Brathwaite and Devon Smith having been sent packing by Morkel and Vernon Philander respectively the previous evening.
But it was not long before the rampant Steyn, who had limped off the park on Friday with a groin problem, took charge, having Johnson (39), Shivnarine Chanderpaul (4), Marlon Samuels (17) and Denesh Ramdin (4) all caught out.
Windies skipper Ramdin lasted just two balls before edging off the shoulder of his bat to diving wicketkeeper AB de Villiers, who had previously pouched both Johnson and Chanderpaul.
Morkel then got in on the act when his on-the-up delivery was clipped by Jermaine Blackwood (17 off 15 balls) to substitute fielder Temba Bavuma at short leg to leave Ramdin???s charges on 117-7.
However, Steyn, who had emerged wicketless from West Indies??? first innings, resumed his onslaught by forcing Jerome Taylor to hit to captain Hashim Amla, South Africa???s double centurion from their 552-5 declared earlier in the game.
The 31-year-old then extinguished the Windes when he dismissed Sheldon Cottrell, with last man Kemar Roach not batting because of an ankle injury.
The tourists??? tame innings meant they lasted fewer than 103 overs in the match, with Johnson???s 39 second time around their highest individual score across their two knocks.
South Africa, though, cemented their position as the top-ranked Test nation and will now be hoping to wrap up the three-match series before the third clash in Cape Town in early January.