The all important goal was scored by defender Debnath following a free kick taken by Sony Norde in the 74th minute.
Bagan finished their league engagement with five points from four matches. Shillong Lajong drew blank from the four matches they have played.
Both the teams played for pride as they were out of the tournament.
Bagan also missed a penalty after Jeje's feeble shot was saved by rival keeper Vishal Kaith who was largely responsible for keeping the slate clean in the first half.
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Luck also was not in Bagan's favour as woodwork twice came in their way twice. Sony Norde's try from top of the box and Kinshuk Dednath header hit the cross bar.
Lajong defence did well with Airbor Khongjee standing tall to thwart rival moves and looking to attack on the counter and nearly succeeded on a couple of occasions but Shilton Paul did well to make saves from David Ngaiate and Rupert Nogrum.
Lajong keeper Vishal spilled the ball from a free kick taken by Sony Norde to give Mohun Bagan their first win and end their campaign on a winning note.