Kohli hit 166* and Gill 116 to power India to 390 while Siraj picked up four as Sri Lanka were bowled out for 73.
India wrap up Sri Lanka ODI series with four-wicket win at Eden Gardens with a game to spare.
Sri Lanka finished strong with Shanaka ton but India managed to hold on to win by 67 runs.
Sri Lanka start quickly in steep chase before hosts trigger middle-order collapse.
Sri Lanka survive Axar blitz but they beat India by 16 runs in second T20I, series levelled 1-1.
Wicketkeeper batter Sanju Samson has been ruled out of the two remaining T20Is against Sri Lanka.
Chasing a target of 163, Sri Lanka could make 160 runs as India win by 2 runs in thrilling 1st T20 at Mumbai.
Rohit returns as India pull selection surprise for Sri Lanka matches.
Sri Lanka will be touring India from January 3 to January 15 for three T20Is and three ODIs.
The Australia tour of India for the Border-Gavaskar Trophy will kickstart in Nagpur on February 9.