Mohammed Shami and Ravindra Jadeja took nine wickets between them as India outplayed South Africa, winning by 203 runs on the final day of the first Test on Sunday.
Set a daunting target of 395, the tourists were bundled out for 191 in the second session in Visakhapatnam, giving India a 1-0 lead in the three-match series.
Shami returned figures of 5-35 while Jadeja took four wickets to help current leaders India grab 40 points in the World Test Championship.
"These... of conditions are pretty ideal for him (Shami). He knows how to bowl on (these) pitches, gets reverse swing straight into play once he knows there is some help on offer," said Rohit Sharma, named man of the match for hitting two centuries in the game, which was his first as an opener.
"He has mastered that art (of reverse swing) now, bowling with the old ball and getting it to reverse."
South Africa were staring down the barrel at 70-8 but Dane Piedt (56) and debutant Senuran Muthusamy (49 not out) put on 91 runs for the ninth wicket to frustrate the Indian bowlers briefly.
Shami got last man Kagiso Rabada caught behind for 18 to trigger celebrations in the Indian camp.
Sharma put India in a commanding position with a century in each innings on his debut as a Test opener -- a first by any batsman in Test history.
His knocks of 176 and 127, coupled with a fine 215-run innings by Mayank Agarwal, helped India put India in a commanding position.
"Once you have 500 on the board, it's difficult for the opposition. Mayank and Rohit played brilliantly," India skipper Virat Kohli said.
Shami took three key wickets in the morning session including that of skipper Faf du Plessis for 13 to dim South Africa's hopes of saving the game.
Jadeja soon joined forces to run through the middle order with three wickets in one over including that of overnight batsman Aiden Markram (39) with a one-handed return catch.
The Proteas resumed the day on 11 for one and soon the batting came under attack by some inspired Indian bowling on a pitch that offered variable bounce.
Off-spinner Ravichandran Ashwin struck first to clean up overnight batsman Theunis de Bruyn for 10, becoming the joint-fastest to 350 wickets in his 66th Test.
Ashwin, who claimed eight wickets in the match and registered his 27th five-wicket haul on Friday, now shares the feat with Sri Lankan legend Muttiah Muralitharan.
He finished the game with eight wickets.
- Sixes galore -
Shami continued with his exploits, bowling Temba Bavuma for nought on a delivery that stayed low.
The veteran paceman came back in his second spell to rattle the stumps of captain du Plessis, who was leaving the incoming delivery, and Quinton de Kock for zero.
The match also witnessed the most number of sixes -- 37 from four innings -- surpassing the 35 that were smashed in a game between Pakistan and New Zealand in 2014-15.
Sharma -- India's limited-overs star -- got 13 of those sixes, the most in a five-day game by one batsman, breaking Wasim Akram's record of 12 for Pakistan.
South African opener Elgar also made an impression with his 160 in his team's first innings total of 431 that appeared to bring the visitors back in the game.
"I thought up until this morning we competed really well," du Plessis said of the loss.
"On a day five pitch, things happen quicker, but it's the nature of Test cricket."
The second Test will begin on October 10 in Pune.
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