The versatile player who can play both in defence and in midfield has signed a deal till 2023.
Chennaiyin FC finished the season with 20 points from as many games.
Three teams – Hyderabad FC, FC Goa and NorthEast — are tied on 27 points from 18 games, intensifying the race for the last two play-offs spots.
The draw, Goa's sixth on the trot, helped the Gaurs climb to the third spot on the table.
The opening half proved to be a cagey contest with both the sides displaying great defensive organisation.
Coach Csaba Laszlo's side put up a spirited performance but their misfiring attack couldn't get past Bengaluru keeper Gurpreet Singh Sandhu.
The result meant the Islanders extended their unbeaten run to 12 games, matching FC Goa's record.
Tiri made a goalline clearance to deny Chennaiyin FC and take ATK Bagan two points shy of leaders Mumbai City FC (26 points) who have a match in hand.
Goncalves scored in the 15th and 21st minutes for Chennayin before Diego Mauricio struck a screamer in the 64h minute to give Odisha some hope.
Chennaiyin FC and Odisha FC played out a goalless draw in the early kick-off.