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.
The match saw both teams failing to convert clear-cut chances. That Odisha had three shots on target while Chennaiyin managed just two exemplified how much both sides cancelled out each other.
Diego Mauricio's second-half brace (50', 60') then settled the tie in favour of Odisha. Gary Hooper (79') scored a consolation for Kerala, but it proved to be not enough to spark a comeback.
NorthEast nearly scored the winner in the dying minutes but substitute Khassa Camara's long-range strike missed the crossbar by inches.
Krishna (90+5'), netted his third goal in as many games to ensure the Mariners climbed to the top of the ISL table.
ISL 2020-21 Gameweek 2 talking points: Impressive ATK Mohun Bagan, Hyderabad FC's defensive resilience and more
Three out of five matches in the second round of ISL fixtures ended in draws, with only ATK Mohun Bagan and Mumbai City FC winning. Here are the talking points.
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
ISL 2020-21: Aridane Santana's solitary goal sees Hyderabad FC begin campaign with win over Odisha FC
Santana converted the spot-kick in the 35th minute as Hyderabad kept their first-ever clean sheet in the league in their second season.
Mauricio made his senior club debut for Brazil's Flamengo in 2010 where he linked up with football legend, Ronaldinho. He has played for other Brazilian teams like Sport Club do Recife, Bragantino and Centro Sportivo Alagoano