Whitewashed in the three-test series and blanked 5-0 in the preceding one-dayers, Sri Lanka posted 170-7, a total they hoped would be enough to end the string of losses which has enraged their fans and prompted the selectors to resign en masse.
There was no respite for them, however, as Kohli blasted 82 and Manish Pandey smashed 51 not out to help India romp home with four balls to spare.
Earlier, Dilshan Munaweera clobbered four sixes in his 29-ball 53 and Ashan Priyanjan, playing his first Twenty20 International, chipped in with a run-a-ball 40 not out to help the hosts post a competitive total after being put in.
India's spin duo of Yuzvendra Chahal (3-43) and Kuldeep Yadav (2-20) shared five wickets between them to restrict Sri Lanka to just under the 175-mark.
Kohli has built up a formidable batting reputation while chasing and the India captain once again came up with a 54-ball masterclass, hitting seven boundaries and a six, to anchor India's chase.
India needed 10 runs to win when Kohli eventually fell in the penultimate over and Pandey sealed victory with a boundary which also brought up his fifty.
(Reporting by Amlan Chakraborty in New Delhi; Editing by Clare Fallon)
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