Chasing a mammoth target of 481 runs, the visitors were bowled out for 143.
For South Africa, AB de Villiers was the highest scorer with 43 runs off 297 balls.
India’s off-spinner Ravichandran Ashwin was the pick of the bowlers with 5/61 in 49.1 overs.
He was assisted by pacer Umesh Yadav (3/9 in 21 overs) and left-arm spinner Ravindra Jadeja (2/26 in 46 overs).
India won the first Test by 108 runs at Mohali and the third match by 124 runs in Nagpur. The second match at Bengaluru was rained off.
Following is the scoreboard on the final day of the fourth and final cricket Test between India and South Africa at the Ferozeshah Kotla here on Monday.
India (first innings) 334
South Africa (first innings) 121
India (second innings) 267/5 Dec
South Africa (second innings) (overnight 72/2)
Dean Elgar c Rahane b Ashwin 4
Temba Bavuma b Ashwin 34
Hashim Amla b Jadeja 25
AB de Villiers c Jadeja b Ashwin 43
Faf du Plessis lbw b Jadeja 10
JP Duminy lbw b Ashwin 0
Dane Vilas b Yadav 13
Kyle Abbott b Yadav 0
Dane Piedt c Saha b Yadav 1
Morne Morkel b Ashwin 2
Imran Tahir not out 0
Extras (b 8, lb 3) 11
Total (all out in 143.1 overs) 143
Fall of wickets: 1-5 (Elgar, 3.6 overs), 2-49 (Bavuma, 42.4), 3-76 (Amla, 84.5), 4-111 (Du Plessis, 119.6), 5-112 (Duminy, 124.2), 6-136 (Vilas, 138.5), 7-136 (De Villiers, 139.1), 8-140 (Abbott, 140.6), 9-143 (Piedt, 142.5), 10-143 (Morkel, 143.1)
Bowling:
Ishant Sharma 20-12-23-0
Ravichandran Ashwin 49.1-26-61-5
Ravindra Jadeja 46-33-26-2
Umesh Yadav 21-16-9-3
Shikhar Dhawan 3-1-9-0
Murali Vijay 2-0-2-0
Virat Kohli 1-1-0-0
Cheteshwar Pujara 1-0-2-0
(IANS)