After a goalless first half, Chennainyin FC created more scoring chances in the second half and the all important goal came in the 52nd minute as the visitors gathered full points.
Chennainyin thus put themselves in a strong position for a place in the play-off after grabbing the third place with 27 points from 15 matches.
FC Goa came back strongly after conceding the goal and had lot of scoring chances but failed to materialise. Luck also did not smile on them as the ball hit the woodwork twice and they remained on the sixth place with 20 points from 14 matches.
Looking for a win to keep themselves in the race for the play-off, both the teams started on an attacking note with Chennainyin creating early chances but first Inigo Calderon failed to find his shot on target and later Raphael Augusto, who troubled the rival defence with speedy run, shot straight to keeper Naveen Kumar.
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Goa, who had a shaky start, slowly settled down and took control over the midfield with Ahmed Jahouh and Eduardo Bedia dictating terms. They tried to make inroads but found stiff challenge from the rival strong defence who thwarted their moves.
It was the host that created dangerous moves and nearly found the net in the 37th minute but keeper twice came to the rescue, parring away Bikramjit Singh cross from the right and off the rebound Jeje Lalpekhlua's powerful shot was blocked by Naveen as both the teams remained goalless at half time.
Soon after the break, Gregory Nelson's cross from the left was tapped in by Jeje but Narayan Das made a goalline save.
The striker crossed across the face of the goal for Inigo Calderon but the ball hit Narayan Das on the goal line and went in.
Down by a goal, FC Goa coach Sergio Lobera made double changes bringing in Hugo Adnan Boumous and Chinglensana Singh in place of Bruno Pinheiro and Narayan Das and they came with flurry of moves.
The home team made desperate attempts to find the equaliser in the last quarter of the match but luck did not smile on them as twice the ball hit the cross bar, first from Manuel Lanzarote's free kick and latter Brandan Fernandes's left footer.