East Bengal are unbeaten in their last six games, and coach Robbie Fowler's team is now just five points below the play-off position.
Goncalves scored in the 15th and 21st minute for Chennayin before Diego Mauricio struck a screamer in the 64h minute to give Odisha some hope.
After suffering six defeats, Odisha notched their maiden win of the season by defeating Kerala Blasters last week. They followed that by securing a draw over the weekend.
Chennaiyin FC are going into the match after their worst display of the season, a 1-4 defeat at the hands of Hyderabad FC.
Poor finishing has cost CFC in the games so far and they have given away goals from set-piece situations which would not please the coach Csaba Laszlo as team has two wins, two losses and four draws so far.
The point from the draw meant that the Kolkata heavyweights (17 points, eight matches) surged past Mumbai City (16 from seven matches) to the top of the table with a one-point lead.
In a game that saw 39 shots at goal, Rahim Ali (53rd minute) scored the match-winner after Jorge Ortiz (9th) cancelled out Rafael Crivellaro's (5th) opener.
ISL 2020-21: Chennaiyin FC face stiff challenge against NorthEast United as they aim to return to winning ways
Despite not getting the results and points their performances have merited, CFC have been arguably one of the most attractive sides to watch, creating a flurry of chances in every game they have played so far.
ISL 2020-21: Sunil Chhetri's penalty against Chennaiyin FC powers Bengaluru FC to first win of the season
A 56th-minute penalty strike from Sunil Chhetri was the difference between the two teams as Chennaiyin suffered their first loss of the season.
ISL 2020-21: Chennaiyin's Jakub Sylvestr misses penalty in stalemate; Odisha fight back to rescue point against Jamshedpur
Chennaiyin missed an excellent opportunity to take lead in the 74th minute when Jakub Sylvestr's penalty was saved by the Blasters custodian Albino Gomes
The CFC coach has said that his team would play high-intensity football this season and going by the way the two-time champions started, the 'Men in Blue' will look to carry on in the same vein.
With Mohun Bagan joining ATK and entry of East Bengal, ISL 2020-21 will be the first season with the biggies from Kolkata. 11 teams will vie for the title when the season begins on 20 November.
It will be the 56-year-old Hungarian Laszlo's first stint in Asia. He has more than two decades of coaching experience at club and international level.