It was the fourth straight win in as many Tests in the World Test Championship for Virat Kohli's men, who also won 2-0 in West Indies, and India have now won 11 consecutive Test series at home.
India maintained their formidable home record by crushing South Africa by an innings and 137 runs in the second Test at Pune to clinch the three-Test series with a match to spare on Sunday.
Made to follow on, South Africa were bundled out for 189 in their second innings in a little over two sessions as the hosts took an unassailable 2-0 lead in the series.
It was the fourth straight win in as many Tests in the World Test Championship for Virat Kohli's men, who also won 2-0 in West Indies, and India have now won 11 consecutive Test series at home.
The last time the world's top-ranked Test side lost a Test series at home was in 2012 when England beat them 2-1.
Replying to India's mammoth first innings total of 601 for five declared, the touring side were all out for 275 at the close of third day's play on Saturday and Kohli decided to put them in again.
The fast bowlers responded to their captain's call with an inspired spell when they swung the new ball prodigiously with South Africa's batsmen looking completely at sea.
Needing to bat the better part of two days to keep alive any hopes of a draw, the touring side got off to a horror start to their second innings when opener Aiden Markram fell for a pair, his second dismissal without scoring in the Test.
His dismissal was identical to his first innings failure and he fell leg before on the second ball he faced from fast bowler Ishant Sharma.
Markram consulted opening partner Dean Elgar but did not review though replays suggested the ball would have missed the stumps.
A nervy Theunis de Bruyn opened his account with a missed run out chance and then Kohli dropped him at slip but the batsman could not make the most of his reprieves.
India wicketkeeper Wriddhiman Saha proved why Kohli thinks he is the best glovesman in the world when he flung to his left to hold on to a one-handed catch to send back de Bruyn for eight off Umesh Yadav.
Elgar and South Africa skipper Faf du Plessis, who made five, combined to hold off India's march with a 49-run stand for the third wicket before the latter was out to Ravichandran Ashwin with Saha juggling the ball before completing the catch.
Ashwin struck again in his next over when Elgar miscued a lofted shot to be caught at mid off for 48.
Temba Bavuma, who made 38, and Quinton de Kock fell to left-arm spinner Ravindra Jadeja before the South African lower order staged a brief resistance.
Vernon Philander and Keshav Maharaj, who combined for 109 in the first innings, added 56 for the eighth wicket to delay India's win before Yadav finally broke the stand when Philander edged one down the leg side to be out for 37.
Yadav and Jadeja took three wickets each for the hosts.
