Left-arm spinner Ravindra Jadeja grabbed five wickets and off-spinner Ravichandran Ashwin took three as the Proteas, set a victory target of 218, were shot out for 109 after tea on the third day.
Both bowlers finished with eight wickets in the low-scoring match played on a dusty, dry pitch at the I.S. Bindra stadium, with the Indian spinners claiming 19 of the 20 South African scalps.
The Proteas were reduced to 60-6 before Stiaan van Zyl, who top-scored with 36, and Simon Harmer (11) got together to put on 42 for the seventh wicket.
Seven batsmen failed to reach double figures, leaving the top-ranked South Africans a lot to ponder ahead of the second Test in the four-match series which starts in Bangalore on November 14.
Indian captain Virat Kohli said he was delighted to win his first Test on home soil as captain.
“This was a special occasion for me,” said Kohli, who turned 27 on the first day of the match.
“Ours is a young team and we are trying to build a strong team together. A lot of credit to the boys for bouncing back after the loss in the limited-overs series.”
‘No demons in pitch’
Kohli said it was wrong to criticise the pitch which produced a three-day Test.
“I don’t think there were any demons in the wicket,” he said. “The ball did not turn square at any stage. Batsmen had to apply themselves since it was a bowler’s game.”
South African skipper Hashim Amla refused to blame the defeat on the pitch, saying there were a few “soft dismissals” by his batsmen.
“200 was a chaseable total, although probably 150 would have been more realistic and a challenge on a deteriorating wicket,” he said.
“There were some soft dismissals. We were in the game till we lost four or five wickets and put pressure on the lower order guys. Stiaan showed you could get runs if you hung in there.
“To get India out for 200 was an excellent effort from our bowlers and we kept ourselves in the game till the last session. But credit to India for bowling us out.”
Earlier, South African spinners Harmer and Imran Tahir claimed four wickets each to rip through India’s batting in the morning session.
India, who started the third day at 125-2 in their second innings, moved to 161-2 before a batting meltdown saw them lose their last eight wickets for 39 runs.
South Africa fared worse when they batted a second time on a wicket that proved to be a batsman’s nightmare.
The gamble to open the batting with tailender Vernon Philander backfired when the fast bowler was leg-before to Jadeja for one in the second over.
Ashwin, who had taken five wickets in the first innings, struck in the third over as Faf du Plessis edged an easy catch to Ajinkya Rahane in the slips.
From 9-2, the Proteas became 32-4 as Jadeja bowled Amla for no score and star batsman AB de Villiers (16) also found his stumps shattered by leg-spinner Amit Mishra.
The wickets continued to tumble as opener Dean Elgar (16) top-edged an intended pull off seamer Varun Aaron and spooned an easy catch to Indian captain Virat Kohli at mid-on.
In the morning, the loss of three top-order batsmen in the space of three runs triggered India’s collapse even though the Proteas fielded without their injured pace spearhead Dale Steyn.
The overnight pair of Cheteshwar Pujara and Kohli batted through the first hour to take their third wicket stand to 66 runs.
The tourists took the field without Steyn, who was sidelined for the entire innings due to a groin strain.