India rode Ajinkya Rahane's cultured century to post a series-high 334 before returning to skittle out South Africa for 121 on Friday to take control of the fourth and final test on Friday.
Rahane (127) crafted the first century in the low-scoring series over five painstaking hours and also featured in a 98-run eighth-wicket stand, the highest in the series, with Ravichandran Ashwin (56).
Spinning allrounder Ravindra Jadeja (5-30) then orchestrated South Africa's rout at the Ferozeshah Kotla stadium as the hosts dominated the second day's play but did not enforce the follow-on.
Indian paceman Umesh Yadav dismissed Dean Elgar (17) to draw first blood but it was Jadeja's triple strike soon after the tea break which unhinged the visitors.
Temba Bavuma (20) dragged a Jadeja delivery onto his stumps, captain Hashim Amla (3) fell after his 34-ball ordeal and Faf du Plessis recorded his third duck of the series after playing an outrageous scoop shot.
The India pacemen, content playing second fiddle to their spin colleagues in the series, drove home the advantage with Yadav uprooting JP Duminy's off stump and Ishant Sharma castling Dane Vilas.
With wickets tumbling at the other end, AB de Villiers waged a lone battle before holing out for 42.
Earlier, India resumed on day two on 7-231 and Rahane, on 89no, stitched a third 50-plus partnership in the match with Ashwin before bringing up his fifth Test century with an immaculate straight drive past fast bowler Kyle Abbott.
An industrious batsman in a line-up teeming with flamboyant stroke players, the 27-year-old raised his arms and looked skywards in a mixed sense of relief and elation, having failed to go past 15 in the series.
Celebration followed with Rahane launching offspinner Dane Piedt over mid-wicket and long-on for two sixes in three deliveries.
The No.5 fell to a soft dismissal, driving Tahir to de Villiers at cover to depart after a stellar knock featuring four sixes and 11 boundaries.
Ashwin, the leading wicket-taker in the series, hit Tahir for a six to bring up his sixth Test 50.
Abbott dismissed Ashwin and Ishant Sharma in three deliveries to finish with 5-40 but the visitors could not stop India posting the first 300-plus score in the series.
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