Ashwin ripped through the top order with 4-8, improving on his own best of 4-11 against Australia at the World Twenty20 two years ago, as Sri Lanka was bowled out in only 18 overs for 82, its lowest T20 total.
In reply, India reached 84-1 in only 13.5 overs with opener Shikhar Dhawan top-scoring in the third and final match with an unbeaten 46.
Ashwin drew first blood with his third delivery as a vicious spinner beat left-handed opener Niroshan Dickwella (1) for Mahendra Singh Dhoni to complete an easy stumping. The spin bowler then trapped Tillakaratne Dilshan leg-before wicket off the last ball of the over to trigger a collapse.
Captain Dinesh Chandimal (8) fell to the first delivery of Ashwin's second over, caught on the off side while trying to clear the infield. Debutant Asela Gunaratne (4) was his fourth victim, caught at leg slip by Suresh Raina as Ashwin finished his three-over spell at 4-5 and the score at 20-4.
"I want to keep the batsmen guessing and (getting) wickets makes me a different bowler," Ashwin said. "I've the courage to go for runs, that's why I've the courage to flight the ball."
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Indian cricketers Shikhar Dhawan, left, and Ajinkya …
Indian cricketers Shikhar Dhawan, left, and Ajinkya Rahane greet each other to celebrate their victo …
With Ashish Nehra dismissing Milinda Siriwardana (4) soon after, Sri Lanka was reduced to 21-5 in just over five overs.
Dasun Shanaka (19) and Thisara Perera (12) were the only ones to reach double-figures with the batsmen playing rash shots rather than try to play out the overs despite the loss of so many wickets.
"We didn't perform well throughout the series as batsmen," Chandimal said. "If we had got 140-plus runs, we would have had a chance, but we didn't do that. Losing wickets happens with an inexperienced team. We need to regroup as a team."
India made a steady charge toward the target as Dhawan followed up his 25-ball 51 in the previous game at Ranchi. This time, he managed a run-a-ball knock during which he added 55 runs for the unbroken second wicket stand with Ajinkya Rahane (22 not out).
"We opted to bowl first so it was important to restrict them," India captain Dhoni said. "It's always good to have the conditions suiting you and to have the resources to exploit the conditions. The consistency will give us the confidence to play freely."
Ashwin to debut in county cricket