Churchill Brothers dominated the first 40 minutes with captain Anthony Wolfe (7th) and Ansumana Kromah (34th) handing a stunning 2-0 lead.
But Willis Plaza's introduction as a 36th minute substitution stepped up the home team's tempo as they finally pulled one back when Chris Payne (67th) fired one into the far corner after being fed by Robin Singh.
This was a third win for the Goans in their last four outings after Derick Pereira took over as coach as they looked to break into top five. They now trailed fourth and fifth placed Bengaluru FC (16) and Shillong Lajong (16) by one point.
This was East Bengal's second defeat this season.
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Churchill skipper and Trinidadian forward, Wolfe, easily slotted the ball home in front of an open net after goalkeeper TP Rehenesh and defender Anwar Ali made a blunder.
By the 51st minute, East Bengal had used all their substitutes with Morgan showing a sense of urgency by bringing a fit-again Plaza from the bench.
East Bengal looked a transformed side in the second half but could not make use of any of the opportunity.
In the 89th minute, a regulation corner from Mehtab Hossain had them a chance with Plaza almost sneaking in before Churchill substitute Pankaj Sona made a goal-line save.
East Bengal also survived an injury scare when their central defender Arnab Mondal collided with Wolfe in the 56th minute. Mondal needed bandage on his head but he was back on the pitch in a few minutes.
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