South Africa's stubborn effort at the crease eventually came to nothing as India have wrapped up the fourth Test by 337 runs in Delhi, sealing the series 3-0.
AB de Villiers led the way at the start of day five as the Proteas searched for a surprise draw, but India took the eight wickets that they needed to secure the win.
The hosts looked certain for victory when they declared on 267-5 in their second innings, but the Proteas frustrated with the bat by forcing the Test into a fifth day.
South Africa began the morning on 72-2 and they battled to tea on 136-5, losing Hashim Amla (25), Faf du Plessis (10) and Jean-Paul Duminy, who was dismissed for a duck.
An unlikely draw began to look possible as South Africa had the slowest run-rate in stands of over 200 balls, but the evening session belonged to India's bowlers as Umesh Yadav took three wickets and Ravichandran Ashwin dismissed two to ensure victory for the hosts.
Yadav bowled out Dane Vilas for 13, and Kyle Abbott suffered the same fate but for a duck, while Dane Piedt was caught out by Wriddhiman Saha for one.
The key wicket came when De Villiers was caught by Ravindra Jadeja off the bowling of Ashwin, resulting in the South African walking away with 43 runs off 297 balls.
Ashwin wrapped up the match for India, who are now second in the ICC Test rankings, by bowling out Morne Morkel for one.
The Proteas' 14.78 runs per wicket is their lowest in a series since 1912 against England.
