Dempo, who led 1-1 in the first half, scored through Clifford Miranda (37th), Ranty Martins (50th), Koko Sakibo (63rd) and substitute Rowilson Rodrigues (85th).
Roberto Silva scored a brace to reduce the margin for Churchill Brothers.
With the win, Dempo extended their lead over their nearest rivals Mohun Bagan and Pune FC by seven points. Churchill Brothers remained on 41 points from 23 matches.
It was a crucial match for both teams as Churchill Brothers needed a win to keep their hope alive to clinch the title. On the other hand, Dempo wanted to extend their lead and take a firm grip to win the title for the fifth time.
Dempo, after coming close to scoring twice, took the lead in the 37th minute. A quick build-up in the middle between Martins and Sakibo saw the later release the ball to Miranda on the left flank. Miranda quickly positioned himself and unleashed a firm left-footer that found the net.
Churchill regrouped and equalised minutes before the interval through Roberto Silva.
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After the change over, Roberto Silva put Churchill Brothers ahead in the 46th minute. But Dempo soon found the equaliser in the 50th minute when Martins uncorked a low shot from top of the box that left keeper Arindam Bhattacharya rooted on the ground.
Dempo then struck in the 63rd and 85th minute through Sakibo and substitute Rodrigues respectively to settle the matter in their favour. PTI MCS RSY AT