The chief architect of ATK's splendid win was the South African medio Samheeg Doutie who produced a stunning brace (20th and 78th), beside setting up captain Borja Fernandez (22nd) with a superb assist at the Vivekananda Yuva Bharati Krirangan.
Former Canada International Iain Hume (68t) struck from a penalty to bring up his sixth goal of the season after Doutie was brought down inside the box.
For Goa, it was their second loss by an identical scoreline as they had lost to Chennai 0-4 at home earlier.
Having won 7-0 at home Goans were high on confidence but ATK coach Antonio Habas had yesterday reminded the visitors that "it was history and anything can happen in football".
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Habas' boys lived up to the coach's words as they did not allow an inch to the Goans and kept their invincible record intact.
Earlier, the rampaging Goans on a high after their record win against Mumbai were off to a brisk start as Leo Moura and Dudu Omagbemi getting back to back chances to start the match.
Capitalising on a shaky defence from Mondal who had faltered in the beginning, Moura failed to keep his shot down inside the box as the ball sailed behind.
Four minutes later, FCG had a good opportunity with Dudu up front as the Nigerian intercepted Mondal's back pass before launching a powerful shot into the far post where ATK goalkeeper Amrinder Singh did well to thwart his effort to give the packed home fans some sigh of relief.
Allowing FCG little breathing space, Gavilan evaded Jonatan in the same move and played it for the Canadian International Hume whose effort just missed the far post.
Having raised their game and denying the Goans any possession, it was time for some fireworks as the Doutie put the home team into the lead before assisting another to double the lead in less than two minutes.
It was the Spanish medio Gavilan who set up the goal from a thow-in as Doutie dribbled through the Goan defence to put into the far corner, and what followed were his acrobatic somersaults to loud cheers from the home team.
Waiting on the edge of the box, Fernandez blasted it with his powerful rightfooter into the top left corner to virtually seal the match for them.
This was the former Real Madrid player's only second goal in the ISL, having scored his first goal in the franchise- based tournament's opener versus Mumbai.
ATK almost tripled the lead three minutes later but Mohammad Rafique made a mess of a fine set up by Fernandez.
In the 78th minute, Doutie made a good run in behind and latched onto Ofentse Nato's pass before rolling the ball into the empty net to bring up his brace and complete the rout.
Both teams made a couple of changes to their starting lineup.
Nato and Mohammed Rafique replaced Arata Izumi and Valdo. For FC Goa, Mandar Dessai and Romeo Fernandes were replaced by Narayan Das and Nicolau Colaco.