India took the final two South Africa wickets in consecutive balls to win the third Test by an innings and 202 runs and secure a 3-0 series whitewash.
The Proteas added only one run to their overnight total and survived just two overs on day four in Ranchi before falling to 133 all out.
Debutant spinner Shahbaz Nadeem removed Theunis de Bruyn and Lungi Ngidi with the final two balls of his first over.
India secured a record 11th straight home Test win in the second Test.
World number one Test side India have also extended their lead at the top of the ICC World Test Championship, having won all five of their matches across two series to claim the maximum 240 points.
New Zealand and Sri Lanka are next on 60 points.
"We believe we can win anywhere," said India captain Virat Kohli, whose side's last Test series defeat was in England last year.
"We've wanted to be the best team in Test cricket, and as long as we compete, things will work out well for us."
De Bruyn, playing as a concussion substitute for Dean Elgar who withdrew from the Test after being hit by a bouncer on day three, made 30 before he edged slow left-armer Nadeem behind to wicketkeeper Wriddhiman Saha.
Ngidi then fell for a remarkable first-ball duck, his shot rebounding up off team-mate Anrich Nortje at the non-striker's end to allow Nadeem to complete the caught and bowled chance.
The visitors struggled with the bat throughout the series after making 431 in the first innings of the first Test, with 133 their lowest score of the series.
"Every Test, we made more mistakes," said South Africa captain Faf du Plessis.
"But we have to give credit to the Indian team - they were ruthless and they were better than us in every department."
Rohit Sharma, in his first run as an opener in Tests, was named man of the series after scoring 529 runs at an average of 132.25, including a maiden Test double century in Ranchi.
India are set to host Bangladesh in two Tests next month, while South Africa's next Test series will be when they host England for four matches in December and January.