Fast bowler Mohammed Shami picked up a five-wicket haul while left-arm spinner Ravindra Jadeja took four in South Africa's second innings to bowl India to a comprehensive 203-run victory in the opening test at Visakhapatnam on Sunday.
Chasing an improbable 395 for victory, the tourists were all out for 191 in the second session after resuming on 11 for one on the final day.
After Rohit Sharma registered twin hundreds in his maiden match as a test opener to set up India's push for victory, the hosts' bowlers put in a clinical performance in the second innings.
Shami snuffed out South Africa's hopes of salvaging a draw with his early strikes and returned later to complete his fifth five-wicket haul in tests.
Jadeja picked up 4-87, including three in one over, to help India take a 1-0 lead in the three-match series.
Tailender Dane Piedt and debutant all-rounder Senuran Muthusamy showed the grit and determination that was missing from their top and middle order batsmen, stitching together a ninth-wicket stand of 91 to delay India's victory.
It was left to Shami, who took 5-35, to break the stand by dismissing Piedt for his fourth bowled-out victim after the batsman had completed his maiden half-century in tests.
Ravichandran Ashwin, who took 31 wickets in four tests to lead India to a 3-0 series win the last time South Africa toured India in 2015, provided the early breakthrough on Sunday when Theunis de Bruyn chopped on the off-spinner to be out for 10.
It tied Ashwin for the fastest in the world to 350 test wickets with Sri Lankan spinning great Muttiah Muralitharan who also achieved the feat in his 66th match.
With the spinners taking nine out of 10 wickets in the first innings on a turning pitch where a few deliveries kept low, Shami displayed what it takes for a fast bowler to succeed on such a surface.
He bowled fast and attacked the stumps and was rewarded with three bowled-out dismissals.
While the ball stayed a touch low to rattle Temba Bavuma's timber, South Africa captain Faf du Plessis was out for 13 to a horror judgement when he shouldered armed to a Shami delivery that came in and hit the off stump.
First innings centurion Quinton de Kock was out for a second ball duck when Shami breached his defence.
Jadeja then got in on the act and reaped benefits for his accuracy on a favourable surface.
He dismissed Markram with a stunning one-handed return catch, and then Vernon Philander and Keshav Maharaj all in the space of five deliveries to jolt South Africa.
It was the third straight win in as many matches for top-ranked side India in the World Test Championships. The second test starts at Pune from Thursday.