The hosts restricted the visitors to a modest 135 and then hit off the required runs in 19.2 overs to claim a hard-fought victory.
India were beaten by a last-ball six when Eoin Morgan blasted medium-pacer Ashok Dinda back in 2012 as T20 International cricket made its debut at this stadium.
That loss to England by six wickets happened three days before Christmas, as compared to the Yuletide-eve victory on Sunday over the hapless Lanka who are heading back home by catching an early morning flight, having lost both the Test and ODI rubbers to the home team earlier.
The second T20 International featuring India at this stadium had also ended in heart-break for the hosts who lost to eventual champions West Indies by seven wickets on March31, 2016 in the semi finals of the World T20 Championship.
Lendl Simmons, who was caught off a no-ball bowled by Ravichandran Ashwin early in his innings, played a match-winning knock of 82 off 51 balls to help Windies successfully chase a stiff target of 193 with two balls to spare.
The close victory achieved on Sunday was India's seventh successive win over the Emerald Islanders in the T20 format after losing the opening game of the three-game series in 2016 at Pune.