In a high-scoring encounter played before a sell-out crowd of 23,000 at the picturesque venue, the tourists chased down India’s challenging 199-5 with two deliveries to spare.
India’s innings after being sent in to bat revolved around a superb 106 off 66 balls by opener Rohit Sharma, ably supported by Virat Kohli’s 27-ball 43.
But the Proteas, helped by the Indian bowlers’ inability to grip the ball in the evening dew, made light of the stiff target following a rip-roaring opening stand of 77 from 53 balls between Hashim Amla and AB de Villiers.
Amla hit 36 off 24 balls and de Villiers contributed a typically aggressive 51 from 32 deliveries that included seven fours and a six.
India claimed three wickets for 15 runs to reduce South Africa to 95-3, but JP Duminy and Farhaan Behardien stepped in to hit a match-winning partnership of 105 that came off just 55 balls.
Left-handed Duminy returned unbeaten on a 34-ball 68 that was studded with seven sixes, three off them from successive deliveries by left-arm spinner Axar Patel.
Behardien chipped in with 32 not out.
Indian captain Mahendra Singh Dhoni said his team had enough runs on the board, but the dew and a few expensive overs by the bowlers proved costly.
“A score of 200 in a T20 game is a good one, we could not have expected more,” said Dhoni. “But there were periods when we conceded too many runs.
“The conditions were not easy for bowling. The execution had to be spot-on, but unfortunately some of our overs went for too many runs.
“In a situation like this, one has to choke the opposition for runs. That did not happen.”
South African skipper Faf du Plessis agreed the wet outfield in the night session helped the batsmen.
“I think it did get a little wet towards the end,” he said. “But what a great game of cricket it was, with both sides getting big totals.
“It was a superb innings from Rohit (Sharma) at the start. But today was one of those days when the bowlers were under the pump. JP (Duminy) was great, he paced the innings so well with good support from Behardien.”
Sreenath Aravind, a 31-year-old left-arm seamer from Karnataka, made a forgettable international debut as he was hammered for 44 runs in 3.4 overs, including a last-over six by Duminy.
In India’s innings, Sharma plundered 12 boundaries and five sixes in his maiden T20 century, displaying a spectacular array of strokes all round the ground.
Kohli became the first Indian batsman to score 1,000 T20 runs as he blazed his way to three sixes and a four.
The pair put on 138 off 74 balls for the second wicket after Shikhar Dhawan was run out for three attempting a second run.
India were coasting at 160-1 in the 16th over before the tourists hit back with four wickets in the final overs.
The second match will be played in Cuttack on Monday and the third in Kolkata next Thursday.
South Africa will also play five one-day internationals and four Tests during their 10-week tour of India.