Chasing 265 for win, the islanders rode on the 36-year-old's master class to complete the task with four balls to spare at the Khan Shaheb Osman Ali Stadium.
The win helped Sri Lanka jump to the top of table in the five-nation continental tournament.
With Shikhar Dhawan (94) and Virat Kohli (48) taking India to 264 for nine after being sent into bat, Sri Lanka were cruising at 134 for one after the butterfingered Indian fielders dropped three catches.
But Ravindra Jadeja, who scalped two wickets in two balls en route to 3/30 and Ravichandran Aswhin (2/42), brought back the Indians. However, Sangakkara stood firm till the penultimate over, in the process striking 12 boundaries and a six.
Continuing his dream run in Bangladesh that include one triple century, three centuries and two half-centuries across Test and ODI formats, Sangakkara looked in complete control even as he lacked support at the other end, after the departure of Kusal Perera (64).  

Statistical highlights:  

# Ajantha Mendis has bagged 21 wickets at an average of 9.76 in six Asia Cup games with a strike rate of 14.8.
# Mendis is the fourth Sri Lankan bowler to capture 20 wickets or more at the Asia Cup, joining Muttiah Muralitharan (30), Chaminda Vaas (23) and Sanath Jayasuriya (22).
# Mendis has taken four wickets or more four times in six games in the Asia Cup. In the Asia Cup final against India at Karachi on July 6, 2008, he had bagged six for 13.
# Virat Kohli has appeared in 100 ODIs in a row to become the third Indian player after Sachin Tendulkar (185) and Mohammad Azharuddin (126) to achieve the feat.
# Kohli, in the course of his 48, has completed his 1500 runs against Sri Lanka in ODIs -- his tally being 1527 runs at an average of 52.65 in 35 matches.
# Kohli is one of the eight Indian batsmen to manage 1500 runs or more against Sri Lanka in ODIs.
# Kohli's record as captain is quite impressive in ODIs - his tally being 516 runs (ave.73.71) in eight innings, including three hundreds and a fifty.
# Shikhar Dhawan (94 off 114 balls) has posted his highest score against Sri Lanka in ODIs, bettering the 68 at Cardiff on June 20, 2013.
# Dhawan's knock is his highest score at the Asia Cup. He became the fifth Indian player to get out in the nervous nineties at the Asia Cup. Sachin Tendulkar (93 vs Sri Lanka at Dhaka on June 1, 2000); Ajay Jadeja (93 vs Pakistan at Dhaka on June 3, 2000); Gautam Gambhir (90 vs Bangladesh at Karachi on June 28, 2008) and Mohammad Azharuddin (90 not out vs Sri Lanka at Sharjah on April 14, 1995) had previously registered scores in the 90s.
# Dhawan has recorded his sixth fifty in ODIs – his second against Sri Lanka.
# Sachithra Madhushanka Senanayake (3/41) has registered his best bowling figures in ODIs.
# Sri Lanka have won 10 and lost nine out of 19 ODIs contested against India at the Asia Cup.
# Sangakkara has received his 25th Man of the Match award in ODIs. His tally accounts for four against India.
# Sangakkara (103 off 84 balls) has recorded his 18th century in ODIs -- his sixth vs India.

# Sangakkara has 12 hundreds to his credit in a winning cause and six in a losing cause in ODIs. His magnificent strike rate of 122.61 during his innings is his second highest in ODIs when he has registered a hundred. During his innings of 169 off 137 balls against South Africa at Colombo (RPS) on July 20, 2013, his strike rate was 123.35.
# Sangakkara became the third batsman to post six hundreds or more against India in ODIs, joining Sanath Jayasuriya (7) and Ricky Ponting (6).
# Sangakkara's ODI batting record since January 2013 is splendid - his tally being 1507 at an average of 65.52 in 29 ODIs, including four hundreds and 11 fifties. Virat Kohli is the only one to amass more runs than Sangakkara during this period -- his tally being 1743 runs at an average of 56.22 in 41 matches.
# A number eleven batsman has recorded two sixes or more 11 times in an ODI. Mohammed Shami's unbeaten innings of 14 off seven balls had two sixes.
# Ravindra Jadeja (3/30) has registered his best bowling performance at the Asia Cup.
# Ravichandran Ashwin became the 17th Indian bowler to complete 100 wickets or more in ODIs.
# Shami (10-0-81-3) conceded 80 runs or more in an ODI for the second time - the first instance was 10-0-84-2 vs New Zealand at Auckland on January 25, 2014.
# Only Zaheer Khan has conceded more runs for India against Sri Lanka in an ODI - 10-0-88-0 at Rajkot on December 15, 2009. Ashish Nehra had figures of 10-0-81-1 in the same game.
# Spinners have captured eight wickets or more against India in an ODI for the fifth time.


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