Sangakkara played the decisive hand in the final with an unbeaten 52 off 35 balls, his first significant contribution of the tournament after four previous innings had brought just 19 runs, and he was delighted to have been able to repay his team-mates while also ending Sri Lanka's time as bridesmaids in major events since 1996.
"It's been a long time coming, I can't be happier or prouder," Sangakkara said. "I think the side carried me so I was pretty happy I could give something back to them. It means a lot to all of us; to me, to our families, to everyone back home."
Jayawardene, who made 24 before finding midwicket which appeared to give India an opening, admitted there had been added emotions around this match
"We finally managed to break the jinx," he said. "Thanks so much to family and friends but this one is for Sri Lanka fans who have been waiting since 1996. It wasn't a normal match. There were a lot of emotions as this was the last T20. It hasn't sunk in yet and it will take a couple of days to get the feeling."
Lasith Malinga, Sri Lanka's captain for the final three matches of the tournament following Dinesh Chandimal's suspension and then his omission, said the team were desperate to give Sangakkara and Jayawardene a victorious send-off from the format.
"I was really lucky to captain in the last three games. Today, we thought it was Sanga and Mahela's farewell match, the boys thought we needed to do it for them. Last few overs we bowled really well. Mahela and Sanga are world-class batsmen and it was a good opportunity for us to be able to play with them. They are still playing Tests and ODIs and the younger players need to pick all that they can from the two."