The Gaurs, who went into the game having won 3 out of their 4 games couldn't continue their fine run as two late first-half goals took the wind out of them before a third at the beginning of the second made this a task too tall for Carlos Pena's team to overcome.
On Thursday, FC Goa, currently placed fifth on the points table, will look for their third win when they take on Jamshedpur FC at the Pandit Jawaharlal Nehru Stadium in Fatorda.
Brandon Fernandes put the Gaurs ahead inside the opening ten minutes, and Cleiton Silva equalised for the Torch Bearers from the penalty spot before Edu Bedia's long-range free-kick made it 2-1 in the 94th minute.
Everyone barring four first-team players away on Durand Cup duties joined the contingent which began practice here at the Salvador do Mundo Panchayat Football Ground on Friday.
FC Goa joins Mohammedan Sporting and Bengaluru FC with three points in Group A, even though the latter have a game in hand. Jamshedpur FC is the other team in the Group. The top two teams from each Group qualify for the quarter-finals.