Temba Bavuma's South Africa are aiming for their first test series victory in India in 25 years when the second match starts on Saturday in Guwahati.
The visitors stunned India in a low-scoring first test at Kolkata's Eden Gardens to extend their fine run after being crowned World test champions in June.
The victory was South Africa's first in India since they won the opener of a two-match series in 2010.
South Africa, who recently drew 1-1 in Pakistan, are now chasing a first series win on Indian soil since Hansie Cronje's team triumphed there in 2000.
"We won a World Test Championship final earlier in the year against Australia at Lord's, but this was right up there for us," coach Shukri Conrad said of the Kolkata win.
"Coming to India, playing at Eden Gardens, doing something we haven't done for 15 years, this is right up there.
"What we lack in (ability) we certainly make up in the ability to play as a unit and the resilience that we show. We never give up."
Led by skipper Bavuma, South Africa defied the odds on a turning pitch with inconsistent bounce at Eden Gardens to beat India at their own game of spin.
Bavuma's gritty 55 not out in South Africa's second innings paved the way for a thrilling win inside three days after the tourists bundled out India for 93 in their chase of 124.
Bavuma's half-century was the only fifty between the two teams on a track where bowlers dominated.
South Africa have added Lungi Ngidi to their squad after fellow quick Kagiso Rabada missed the opener with a rib injury and is doubtful for the final match.
Rabada watched his fellow bowlers rattle the Indian batting with spinner Simon Harmer taking a match haul of eight wickets.
GILL TO MISS OUT
India are sweating on the fitness of skipper Shubman Gill as they look to rescue the two-match series.
Gill suffered neck spasms in the first innings and pulled out of the remainder of the first test, spending a night in hospital.
The top-order batsman travelled with the team to the northeastern city of Guwahati but Indian media said he will not play the second match, with vice-captain Rishabh Pant to lead.
India's ploy to have a turning pitch at Eden Gardens has met with severe criticism from pundits after the hosts faltered badly in their chase.
The defeat was India's fourth at home in six tests having been whitewashed by New Zealand 3-0 last year.
"I completely believe that (coach) Gautam Gambhir and his team in India must play on much better wickets than what they played at Eden Gardens," former captain Sourav Ganguly told TV channel India Today.
Gambhir is under pressure after replacing Rahul Dravid following the T20 World Cup triumph last year.
The going has been tough for the former opener, losing nine out of 18 tests since being appointed coach of a team in transition.
Stalwarts Virat Kohli and Rohit Sharma quit T20 cricket after the World Cup win in Barbados and earlier this year called time on their test careers.
Gill was appointed test captain and drew a tough test series in England 2-2 before leading India's 2-0 whitewash of the West Indies at home.
Play in Guwahati at India's newest test venue will start at 9am (3:30am GMT) because of early sunsets, with the order of the session breaks reversed – meaning tea will be before lunch.
