The visitors looked dead and buried after two days at Eden Gardens in Kolkata but bowled the home team all out for just 93 in the second innings to seal a remarkable 30-run win.
Before the clash, Conrad stated that a Test series victory in India would be as big for the Proteas as winning the World Test Championship final that they did at Lord's in June when they beat Australia.
It was their first win in the longest format in India in 15 years - the last coming in 2010 - but a series victory beckons ahead of the second and final Test that starts in Guwahati on Saturday.
The last time a South African team won a Test series in India was in the year 2000 under the captaincy of the late Hansie Cronje.
"This was right up there for us. Coming to India, playing at Eden Gardens, doing something we haven't done for 15 years, this is right up there," Conrad said.
"We won a Test match in Pakistan, we've now won a Test match here but the job's far from done. You don't come to a country to win a Test match, you obviously want to win the series.
"It's important we stay nice and humble and not get too carried away with this. We want to create an environment and a belief in the side that they shouldn't be surprised when they do certain things.
"They shouldn't be surprised when you come to India and beat them. It's tough. And it's a massive achievement, but this is what we're able to do.
"It will do wonders for our psyche and it will do wonders for us going forward."
The Proteas under Conrad, and the captaincy of Temba Bavuma, have done wonders with the Test unit and the head coach puts the success down to just letting the group be themselves.
With no specialist batter having a career average of above 40, the side has become known for not giving up and fighting until the last ball or the last run is scored - as evidenced by the wins in Kolkata and the final Test against Pakistan in Rawalpindi.
"We've really tried to create an environment where, with South Africa being a diverse country with diverse cultures, this change room embraces all of it," Conrad said.
"We've allowed players to be exactly who they are and do things how they want to do things.
"Obviously, we operate with a set of norms and ethics and values as to what's expected of an elite side and a high-performance side but it's like a bunch of mates that are playing together.
"They don't give up. They practise hard. They'll party hard. And more importantly, we've just allowed a culture to develop organically.
"I don't think there's a recipe or a magic wand. All you can ever ask of a team is to fight for every run and stay in the battle. And I think this side does that."
The Proteas produced a comeback for the ages, led by captain Temba Bavuma, to script one of their greatest Test wins after beating India by 30 runs at Eden Garden in Kolkata.
The Proteas' top-order batting again crumbled on a difficult pitch to leave visitors staring down the barrel of a defeat after two days of the first Test against India in Kolkata.
The Proteas had no answers to Jasprit Bumrah as they folded to 159 all out against India on the first day of the first Test at Eden Gardens in Kolkata.
South Africa will begin their two-Test series against India at Eden Gardens in Kolkata on Friday, with captain Temba Bavuma returning to lead the Proteas after recovering from injury.
