Roy Krishna scored the only goal of the game on the 85th minute.
Aiban Dohling conceded a soft penalty in the final five minutes of the match to give Mohun Bagan a vital win tonight.
Mohun Bagan were dominant in the first half of the game but FC Goa did well to come back into the contest with an impressive second-half display.
They will be disappointed to have dropped all three points in the end and it will be interesting to see how they bounce back in their next outing.
Meanwhile, the mariners will be delighted to have grabbed all three points in the end and they are now up to second in the standings with 13 points from six matches.
Mohun Bagan are level on points with Mumbai City FC and they will be hoping to climb to the top of the table in the coming weeks.
Goa had their chances to score the equaliser in the second half but Mohun Bagan held on for all three points in the end.
Saviour Gama had the chance to score the leveller in the dying moments of the game but his shot was tipped over the bar by the Mohun Bagan keeper.
Alberto Noguera came close to scoring for Goa as well but the Mohun Bagan keeper produced an inspiring display to keep his side in front.
The defeat tonight leaves FC Goa 6th in the table with just eight points from six matches and they will have to improve a lot in order to win the Indian Super League this season.
As for Mohan Bagan, they will be hoping to improve on the attacking front in the coming weeks. They have the quality to win the tournament this season and it will be interesting to see if they can improve their performance in the final third in the remaining matches.