The result, though a dead rubber with India already in Sunday's final against Pakistan and Sri Lanka eliminated, extended India's unbeaten run in the tournament.
India, batting first, piled up 202-5 - the first 200-plus total of this year's competition. Abhishek Sharma, the world's top-ranked T20 batter, led the way with a blistering 61 from 31 balls, reaching fifty off just 22 deliveries for his third consecutive half-century.
Sanju Samson added 39, while Tilak Varma's composed 49 not out anchored the innings. Suryakumar Yadav managed only 12 in a continued lean spell, and Shubman Gill fell for four.
Sri Lanka replied in style, thanks to Pathum Nissanka's dazzling 107 - the first individual century of the tournament. He raced to fifty in 25 balls and three figures in just 52, sharing a 127-run stand with Kusal Perera (58).
Despite their explosive start, Sri Lanka finished level at 202-5 after Nissanka was dismissed on the first ball of the final over.
In the Super Over, Arshdeep Singh delivered under pressure, removing two batsmen and conceding only two runs in five balls. India needed just three, and Suryakumar Yadav struck Wanindu Hasaranga's first delivery to the fence to seal victory.
Among the bowlers, Varun Chakravarthy's breakthrough dismissal of Perera ended Sri Lanka's major partnership, while skipper Charith Asalanka claimed Abhishek's wicket.
For India, there were concerns as Hardik Pandya bowled only one over before leaving the field, and Jasprit Bumrah was rested.
Despite those setbacks, India's resilience ensured a thrilling win and maintained momentum ahead of the highly anticipated final against Pakistan.
India top-order batter Ishan Kishan has been ruled out of the second T20I in New Zealand due to a groin strain, with teenage star Vaibhav Sooryavanshi poised to return to the starting XI.
Sri Lanka executed one of the greatest run chases in ODI cricket, overcoming England's mammoth 430-run target in Rawalpindi to secure a remarkable victory.
India earned their highest-ever T20I run chase when they successfully chalked off New Zealand's 225/4 with four wickets remaining in a run-soaked encounter in Christchurch on Thursday night.
Less than eight overs were bowled in the fifth and final T20I between India and West Indies as heavy rain fell in Bengaluru.
