Debutant spinner Shahbaz Nadeem quickly prised out the final two South African batsmen in the second over of the fourth day to guide India to another victory by a margin of more than an innings.
Resuming to bat at their overnight score of 132-8, the Proteas could manage to add only a single run to their total before Nadeem secured the last two wickets in successive balls to complete an emphatic 3-0 whitewash.
Theunis de Bruyn, batting as a concussion substitute for the injured Dean Elgar, was the subject of a brilliant take from behind the stumps by Wriddhiman Saha, returning to perform his wicketkeeping duties after injuring his finger on day three.
De Bruyn's ill-fated cut shot was executed as an afterthought since he had made up his mind to step down the pitch but the under-edge was snaffled excellently by Saha.
Lungi Ngidi, the next man in, perished on the first delivery in peculiar fashion when he smashed a loopy ball straight at his batting partner Anrich Nortje.
The lanky paceman could not get out of the trajectory of the fast-travelling ball as it hit his wrist and tossed up in the air only to be grabbed by Nadeem.
The 30-year-old, who made his Test debut after registering 424 first-class wickets in a long and illustrious career, finished with a match haul of 4-40.
India's huge win by an innings and 202 runs was set up by Rohit Sharma's supreme batting masterclass as he struck the first double century of his Test career and later pacers Umesh Yadav and Mohammed Shami unsettled the South Africa lineup causing their demise.
Sharma's remarkable series with the bat, following his promotion to the opening slot, allowed him to earn the player of the series prize.
India now comfortably sit atop the World Test Championship table, having bagged 240 points after series wins over the West Indies and South Africa.
The timid manner in which Faf du Plessis' men were blown away by India's hegemony at home points towards glaring inherent weaknesses of the Proteas side still in the throes of rebuilding.