World number one side India have an unassailable 2-0 lead in the series heading into the final Test in Ranchi, which starts on 19 October.
Skipper Virat Kohli set up the win with his unbeaten 254 - a record seventh double-century for the star batsman - in India´s 601 for five declared.
The Indian cricket team became the first Test side to make South Africa follow-on since 2008 and also the first Indian team to enforce follow-on in a Test against South Africa.
After being asked to follow-on, South Africa were all-out for 189 in 67.2 overs just after the tea break.
India extend their lead over New Zealand at the top of the ICC World Test Championship, with four wins from four.
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.
After a long discussion with non-striker Elgar, Markram didn't opt for the review but TV replays clearly showed the ball was missing the leg-stump.
Ashwin struck again in his next over when Elgar miscued a lofted shot to be caught at mid off for 48.
Quinton de Kock then perished in tame fashion post the interval but once again, the lower order didn't cave in without putting up a fight.
The duo had accumulated a 109-run partnership in the first innings to help South Africa end their innings on 275 runs.
The 30-year-old Indian skipper scored 254 runs and remained not-out as he chose to declare the innings and make the Proteas bat. Kohli broke many records on day three of the Test as he became the only Indian with seven double centuries in Tests, surpassing Sachin Tendulkar and Virender Sehwag.
"We are lucky to have a group of players we have in the last three-four years".
"In the last three to four years it's unbelievable to see the hunger in this group to keep improving".
Du Plessis, meanwhile, admitted Kohli's knock and India's mammoth total made the tourists play catch-up after the hosts elected to bat first.
"The way India batted, especially Virat, takes a lot of mental toughness. Two days in the field can wear you down", said du Plessis.