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 captain Shubman Gill called on his side to raise their fielding standards and improve their bowling accuracy at the end of the innings after they lost the third ODI against West Indies in New Chandigarh.
Shai Hope struck an unbeaten 162 to help the West Indies record their highest ODI run-chase and beat India by five wickets in the final game of the series on Saturday.
India coach Gautam Gambhir was happy with this side's record ODI run chase on Wednesday night, but did not mince his words when describing the contest.
Shubman Gill struck a double-century as India recorded their highest-ever ODI run-chase to beat West Indies by eight wickets in Guwahati as the hosts sealed the three-match series with a game to spare.
