Eyeing their 14th title, Mohun Bagan had crushed Shillong Lajong 5-0 in the first leg semifinal on May 8 in Barasat.
Mohun Bagan are by far the most successful side in the tournament's 39-year-old history.
The home side, needing a massive win to make the cut for the summit clash, began on an aggressive note, but failed to create too many chances.
Shillong Lajong came close to scoring towards the middle of the first half, but Konsham Chinglensana Singh's header ballooned over from inside the six yard box.
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After the break, Mohun Bagan scripted a brilliant counter attack, with Sony Norde outwitting three rival defenders, and Yusa latching on to the pass. But his pass was squandered by Jeje Lalpekhlua.
The action shifted to the other end, as Bipin Singh's 30 yard free kick saw Bagan custodian Debjit Majumdar fumbling. Shillong's Fabio Pena made a try, but only succeeded in blowing the ball over the bar.
The last time Mohun Bagan won the Federation Cup was in 2008.