On the third day, South Africa improved their first innings score to 408 for a 163-run lead, led by opening batsman Dean Elgar, who will retire after the two-Test series, with 185 and Marco Jansen with a career-best 84 not out.
Proteas pacers dismissed India for 131 runs in 34.1 overs, with only Virat Kohli (76) standing in their way as they stormed to victory.
On his debut, Nandre Burger collected four wickets for 33, taking his total to seven. Meanwhile, fellow left-armer Marco Jansen claimed three wickets for 36, and first-inning hero Kagiso Rabada added two wickets for 32 to his five first-day wickets.
“This win was massive for us and what makes it bigger is that it makes sure India have never beaten us in a Test series here,” Conrad told reporters.
“We know what a quality side India are, but we also know what we are,” the coach said after South Africa’s first innings win over India since 2010 at the same venue.
“We are a brilliant team at home and we have really gelled as a unit. A lot of the time that has been about freeing the guys up, allowing them to be the best versions of themselves.
“People have questioned whether South Africa still produce good players and we have shown that we do.
“Sometimes I think we are too humble, raving about overseas players and not realising what we have.
“These guys are absolutely phenomenal. And we have put succession plans in place. You need a bit of luck and things will fall into place,” Conrad said.
Since his hiring as the red-ball national coach at the beginning of the year, South Africa has won three Tests in a row, snapping a five-match losing skid.
The loss was referred to as “a very upsetting loss” by India captain Rohit Sharma, who also stated that at the Test level, players’ mindsets were what distinguished the good players from the bad.
“Obviously there was a lot we did not do right. We have some inexperienced players and it is all about mental preparation and your plans.
“Even in terms of technique, it comes down to players’ individual plans against certain bowlers.
“KL Rahul was the perfect example in his first-innings hundred of showing intent and respecting the conditions. He had a strike-rate of 70-odd and he put the bad balls away.
“But we cannot just come in and swing our bats, it was not the conditions for that. There is a thin line between intent and discipline, and the players need to show that extra bit of temperament too.
“You cannot just have one mindset of ‘this is how I bat’, you must adapt.
“Jasprit Bumrah bowled well, but all he wanted was a bit of support at the other end, which he did not get.
“Hopefully this will teach us a lot about what we need to do as a bowling group,” Rohit said.
The second and final Test in the series begins on Wednesday at Newlands in Cape Town.
(With AFP inputs)