The first extra time saw no goals but Bengaluru got better of a 10-men FC Goa team 1-0, four minutes from the end of the second extra half.
Rahul Bheke scored the lone goal of the match in the 118th minute to lead Bengaluru FC to their maiden ISL title.
Real Kashmir thanked the ISL club and invited them in March for a friendly fixture, assuring the guests "the most electric football atmosphere".
The win meant Delhi are now unbeaten in their last five matches, winning three of them, while Bengaluru have lost three of their last five matches.
Bengaluru FC have been dominant like last season, while defending champions Chennaiyin have been in woeful form, to say the least.
The result sees Bengaluru extend their lead atop the ISL table to four points, while Kerala Blasters remain winless in 14 matches and are rooted to the ninth spot.
Chencho smashed the second goal for Bengaluru in 71st minute after United striker Federico Gallego got the equaliser in the 60th minute.
Mumbai and Bengaluru are on top of the league table with 27 points each, though Mumbai have played 13 matches, one more than the visitors.
Bengaluru FC are the only team who are unbeaten so far, although they have only played six matches.
Bengaluru broke the Kerala hearts with nine minutes to go. Xisco released Miku into the box and the latter's return was sent goalwards by the Spaniard.
Last season when Bengaluru FC came to Kochi on the eve of New Year, they thumped three goals in what was Rene Meulensteen's final game in charge.
ATK suffered an injury blow to their key forward Kalu Uche in the first-half as they looked desperate to firm up their attacking prowess.
Having suffered back-to-back defeats at home to start their campaign, the new-look ATK have managed to bounce back with two wins and draw.
Youngster Gourav Mukhi made history when he came on for Jamshedpur FC as a substitute and scored on his debut to equalise.
Star forward Cahill is available for selection in Jamshedpur FC, while Dhanachandra Singh will remain unavailable due to his injury woes.
In what was a repeat of last season's final at the same venue, Miku's 41st minute strike was enough for the Blues to overcome the visitors' challenge.
Through Miku's goal in the first half, Bengaluru FC defeated defending champions Chennaiyin FC 1-0.
Bengaluru were the best side in the previous edition, winning 13 of their 18 matches to qualify for the playoffs with four games to spare.
Two goals from Chettri and one each from Rahul Bheke and Nicolas Fedor (Miku) ensured that the early lead taken by East Bengal through Kromah did not stop their march to victory at the Kalinga Stadium.
This was Chennaiyin FC's second title triumph in the ISL, tying them with ATK as the most successful team in the tournament.
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