Mohammed Shami took five wickets as India overcame late South Africa resistance on the final day to win the first Test by 203 runs at Visakhapatnam.
Seamer Shami returned five for 35 while spinner Ravindra Jadeja claimed three wickets in an over to complete figures of four for 87 to dismiss the Proteas, in pursuit of 395, for 191.
Senuran Muthusamy and half-centurion Dane Piedt offered some resistance, recovering from 70 for eight by adding 91 for the ninth wicket, but the damage was already done by Shami and Jadeja.
Ravichandran Ashwin kicked things off, bowling Theunis De Bruyn for 10 to join former Sri Lanka spinner Muttiah Muralitharan as the quickest to claim 350 Test wickets.
Shami then bowled Temba Bavuma, Faf Du Plessis and Quinton De Kock, with Jadeja taking care of Aiden Markram, Vernon Philander and Keshav Maharaj in the 27th over as the tourists crumbled.
India were held up by Muthusamy and Piedt in the afternoon, with knocks of 49 not out and 56 respectively, but Shami returned to wrap up the innings and give the hosts a 1-0 series lead.