FC Goa, who led 2-0 at half time, scored through Romeo Fernandes (33rd minute), Miroslav Slepicka (45+1) and Andre Santos (74th).
The Zico-coached side ended their home campaign with their third straight win and moved to second spot with 18 points from 12 matches to brighten their chances of making it to the semifinals.
NorthEast United FC remained on sixth place at the league standings with 13 points from 12 matches.
Romeo Fernandes infused spark in the match by breaking the deadlock in the 33th minute. Debrata Roy, who initiated the move on the right flank, relayed the ball to Romeo Fernandes who, in turn, laid a pass to Andre Santos inside the box.
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Santos quickly gave a forward pass back to Romeo who after getting the better of defender Miguel Garcia essayed a left footer that hit the post and went in.
The visitors made a substitution bringing in James Keene in place of Kondwani Mtonga and the striker did pose problems to the home team defenders as he came close to scoring twice.
After the change of ends, the visitors made double changes bringing in Tomas Josi and Alen Deory in place of Isaac Chansa and Zodingliana and made some concerted moves with Koke nearly finding the mark.
Jan Seda, who looked confident under the bar, made a rare blemish when he failed to collect a chip from the left, but luckily the ball was cleared by a home team defender for safety.