Kumar Sangakkara hit an important 52 not out in his last Twenty20 international outing to help Sri Lanka chase down the 131-run victory target with 13 balls to spare and deny India, the reigning 50-over World Cup and Champions Trophy winners, a record limited over treble.
"It's been a long time. I can't be happier or prouder because I think the side carried me all the way through to the final. I didn't do much other than keeping wickets," a satisfied Sangakkara said at the presentation ceremony.
"I am pretty happy to be able to do something back for them. It means a lot to all of us."
Sangakkara's crucial 35-ball knock included six boundaries and a six. Another departing great, Mahela Jayawardene, contributed a run-a-ball 24.
Sri Lanka finally managed to break their jinx of losing the finals of global events, having gone down in the decider of the 50-over World Cup in 2007 and 2011 and T20 World Cup in 2009 and 2012
Sunday's final was also a repeat of the 2011 50-over World Cup final which India won in Mumbai.
Put into bat after evening drizzle delayed the start of the all-Asian final by 40 minutes, India posted a below-par 130 for four wickets despite Virat Kohli's breezy 77.
The 2007 winners lost opener Ajinkya Rahane in the second over before Kohli added 60 runs with Rohit Sharma (29) to prop up the innings and prepare for a late assault that failed to materialise.
Yuvraj Singh struggled to find the middle of the bat, taking up 21 balls to score just 11, which coupled with Sri Lanka's brilliant death bowling restricted India to a total that left their bowlers little margin for error.
"In the middle overs, our batsmen tried their best to get going but it was one of those days when we couldn't convert the kind of start we got," India captain Mahendra Singh Dhoni said.
"Virat was the only one who looked fluent but that was after he had played some deliveries.
"We could have always got those 10-15 (extra) runs but cricket is all about those runs."
Kohli, the tournament's top scorer and player of the event, ran himself out on the final delivery of the innings after a 58-ball knock that included four sixes and five boundaries.
Sri Lanka pace spearhead Lasith Malinga dished out plenty of accurate yorkers as India managed just 19 runs off their last four overs.
"It was Mahela and Sanga's farewell match and we had to do something special. All the boys were looking forward to that before the match and that's why we were successful today," captain Malinga said.
(Additional reporting by Sudipto Ganguly; Editing by Pritha Sarkar and Josh Reich)