The all-important goal came in the 15th minute through Jeje Lalpekhlua, which ultimately turned out to be the match winner and helped Dempo move to eighth place with 10 points from eight matches.
Churchill Brothers who are yet to win a match remained on 12th place with three points from eight matches.
Dempo had given an excellent account of themselves in the 3-1 demolition of East Bengal away in Kalyani for their first win in the competition. But the former champions slumped to an unexpected defeat against Bengaluru Football Club, also away, in the next match.
The win will help calm Arthur Papas' nerves going into the fortnight long international break, but it only adds to woes at the other end. Churchill Brothers are now without a win in eight matches and are tied on points (3) with bottom-placed Rangdajied United FC.
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Both the teams knew that a win was a must heading into the break. Dempo coach Arthur Papas did not make too many changes, but was forced to start with Jeje upfront as the lone striker due to an injury to Irish first-choice striker Billy Mehmet.
Two minutes later, Jeje opened Dempo's account after he read Beto's through ball and had all the time in the world to slam the ball past the Churchill goalkeeper.