Ferran Corominas (59', 84'), Edu Bedia (69'), Hugo Boumous (71') and Miguel Palanca (90+1') were on target for the hosts while Bartholomew Ogbeche (90') scored the only goal for NorthEast.
Sergio Lobera made two changes from his side's 2-0 defeat against FC Pune City. Carlos Pena and Jackichand Singh were back in the starting XI in place of Mohamed Ali and the suspended Ahmed Jahouh with Edu Bedia taking the Moroccan's place in holding midfield.
For the visitors, Mislav Komorski's injury meant a start for Gurwinder Singh. The other changes made by Eelco Schattorie were Juan Mascia and Robert Lalthlamuana replacing Keegan Pereira and Lalthathanga Khawlhring respectively.
It took 15 minutes for Goa to create their first clear chance at goal when Brandon Fernandes played Hugo Boumous through on the left, but the latter's goalmouth cross was missed by both Ferran Corominas and Mourtada Fall on the far side.
Minutes later, Brandon's attempt from inside the box was blocked by Gurwinder while Boumous was guilty of failing to tap in a Mandar Rao Dessai's cross from the left. Brandon, too, wasn't able to get on the end of Jackichand's cross from the right as the hosts could have been up by at least a couple of goals ahead of the half-hour mark.
Although NorthEast United didn't manage a single shot on target in the first half, their defensive organisation was adept to survive the onslaught.
Referee Ramaswamy Srikrishna failed to spot the ball coming off Carlos Pena's stray hand in Federico Gallego's corner which was a result of the first time NorthEast had managed a shot at goal when Redeem Tlang was denied by FC Goa goalkeeper Mohammad Nawaz at his near post.
The hosts finally managed to breach the resolve of their opponents in the 59th minute as Corominas stuck out his right foot to divert Jackichand's delivery from the right past rival custodian Pawan Kumar.
Having developed a taste for goal, moments after Brandon forced a save from Pawan, Bedia chipped the ball over a hapless Pawan after Gurwinder failed to intercept Boumous' through the pass in the 69th minute. Soon after, in the 71st minute, Boumous added his name to the scoresheet as he tapped in Brandon's cross from the right.
Corominas would go on to equal Iain Hume's record for the all-time highest goalscorer in the ISL as the Spaniard scored his 28th goal over two seasons when he slotted in a low cross by Boumous from the left in the 84th minute.
NorthEast scored a consolation goal in the last minute of regulation time as Ogbeche fired past Nawaz despite the Goan custodian scooping out the Nigerian's initial effort from a header off Gallego's corner.
However, the Gaurs weren't done yet as Palanca took the ball from Bedia and strolled into the box before drilling a low pile-driver at the back of the net during injury time.