Hyderabad FC scored the opening goal of the game through Aridane Santana on the 58th minute but FC Goa did exceedingly well to mount a splendid comeback late on in the game.
Ishan Pandita scored the equaliser on the 87th minute and Igor Angulo scored the match winner deep into injury time.
The win takes FC Goa up to third in the Indian Super League table just three points behind League leaders ATK Mohun Bagan.
Meanwhile, Hyderabad FC are eighth in the standings with nine points from eight matches.
Hyderabad will be thoroughly disappointed with their result tonight especially after the way they performed until the final five minutes of the game.
They were in complete control and they dominated possession, but Goa managed to fight back with two goals in the space of four minutes.
Hyderabad scored the opening goal of the game when Santana powered in a superb header past Donachie after he was picked out in the box by Ashish Rai.
Substitute Ishan Pandita scored with his first touch of the ball to give Goa some hope and Angulo made the most of a counterattack and cut in from the left to fire the ball past the Hyderabad keeper.
Hyderabad will have to improve on the defensive front if they want to climb up the table in the coming weeks. They could have easily picked up all three points tonight but the lacklustre defending at the end has cost them big time.