Needing only a draw to seal the title, East Bengal took a 24th minute lead when James Moga lobbed the ball over Kalighat M S goalkeeper Shantanu Ghoshal.
Nigerian Edeh Chidi struck in the 77th minute as East Bengal dominated the one-sided match.
In fact, it could have been 3-0 in favour of East Bengal but Ryuji Sueoka's spot kick in the injury time was saved by the KMS goalkeeper.
"The importance of the local league was seemed to be diminishing after the I-League, but not after seeing the euphoric atmosphere today," East Bengal skipper Mehtab Hossain, who is down with an injury, said.
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The side are now three short of breaking their own record of winning the local league six years in a row from 1970 to 1975.
Hossain said the record is something they can break. "Unlike a few of the records created by Sachin Tendulkar, Usain Bolt and Messi, this is definitely achievable. After all, records are meant to be broken."
Today's win has reduced the high-profile local derby against Mohun Bagan in the last round an inconsequential affair as East Bengal now have an unassailable lead of 28 points from 10 matches.
But Hossain said there would not be any let up in intensity against bitter foes Mohun Bagan, winners of 29 local league titles, as a win would be an icing on the cake.
"We have won the title but the pride would be at stake when we face Mohun Bagan. We all will look forward to win against them," the East Bengal playmaker said.