Against Mumbai City FC and ATK, Chennaiyin FC dominated possession and the number of passes.
Besides moving up the table, a win for Bengaluru FC meant maintaining their unbeaten head-to-head record while a Kerala victory would break their duck.
After a 13-day break, two southern rivals — Bengaluru FC and Kerala Blasters — will resume the Indian Super League action at the Sree Kanteerava Stadium on Saturday.
The 2-1 win was made possible by a penalty from Marko Stankovic and a superb free-kick from Marcelinho.
Hugo Boumous (31st minute) put Goa ahead in the first-half before NorthEast United came up with two second-half strikes from Asamoah Gyan (54th) and Redeem Tlang (74th)
The defeat meant that Chennaiyin are yet to find the back of the net so far in three matches this season.
Last year's runner-up FC Goa were a step ahead of their opponents in all areas of the field and were the better team overall.
Bartholomew Ogbeche struck in the 30th and 45th minutes in front of a packed home crowd at the Jawaharlal Nehru Stadium.