With India having already secured their place in Sunday's final against Pakistan and Sri Lanka eliminated, Friday's Super Fours clash was of merely academic interest but it turned out to be the most exciting game of the tournament.
Sri Lanka gave a good account of themselves and matched India's 5-202 to force the Super Over after Nissanka (107) smashed the first individual hundred of the 2025 event.
But Sri Lanka could muster only two runs in the Super Over before losing both their wickets in five deliveries from Arshdeep Singh.
India skipper Suryakumar Yadav then took three runs from the first delivery from Wanindu Hasaranga to seal their victory in a matter-of-fact way.
Earlier, put in to bat, 20-overs world champions India racked up the tournament's first 200-plus total, riding opener Abhishek Sharma's third consecutive fifty in the tournament.
Abhishek, the world's top-ranked T20 batter, maintained his red-hot form with a sizzling 61 off 31 balls.
Opening partner Shubman Gill fell for four and skipper Suryakumar's slump in form continued with just 12 but India did not really suffer as Abhishek raced to a 22-ball  half-century.
Sri Lanka captain Charith Asalanka removed Abhishek but Tilak Varma, who made 49 not out, and Sanju Samson's 39 maintained the pressure on the Sri Lankan bowlers.
In their chase, Sri Lanka lost Kusal Mendis for a duck in the first over but cruised to 1-72 off their six powerplay overs.
India rested pace spearhead Jasprit Bumrah, while Hardik Pandya bowled just one over before leaving the field.
Nissanka needed 25 balls to bring up his fifty and Kusal Perera (58) could not be denied his half-century either.
Spinner Varun Chakravarthy broke the 127-run stand when he dismissed Perera.
Nissanka raced to a 52-ball hundred but fell in the first ball of the last over, which ended with Sri Lanka also on 5-202, forcing the Super Over.
