Into the final minutes and the game tied at 1-1, central defender Gregory, who is a French professional, made it count to score the winner much to the delight of the home fans at the Jawaharlal Nehru Stadium, Fatorda.
But it was Sachin Tendulkar co-owned side, which drew first blood after Mohammed Rafi's 24th in the first half. Rahul Bheke provided the assist from the right flank. It was a delicious loop over the defenders that found Rafi, who nodded it in from point blank range.
It came from a corner which was punched out by the keeper. The ball fell to Moura, who is a professional Brazilian player, just outside the box and he calmly placed it into the top left corner to level the score 1-1 at half-time.
The second half also saw a fierce battle between the two sides as possession moved from bunch to another.
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Kerala Blasters needing a win desperately showed lot of urgency in the second half as they made inroads into the rival half with steady moves. Sanches Watt and Marcus Williams combined well upfront to pose constant threat to the home team defense.
With the match heading into the final 10 minutes, the nervousness between the players of the two sides seemed evident but Gregory came up with a moment of brilliance.
Dempo left-winger Mandar Dessai curled in a beautiful ball from the corner kick towards the middle. The skipper rose the highest to win the header and nod it into the back of the net. Nothing the keeper could do as it was headed with too much power.
The Zico-coached side has 10 points from 5 matches, while Kerala, who slumped to their third consecutive loss, have just four points from five games.