Goals from Marco Sahanek and Antonio Perosevic managed to split the points either way as Khalid Jamil's men ended the season with only three wins.
Jamshedpur defeated NorthEast United 3-2 in the Indian Super League.
NorthEast United scored two late goals to win 2-1 in the Indian Super League.
ATK Mohun Bagan posted a 3-1 win while NorthEast remain rock-bottom.
Jorge Diaz and Alvaro Vazquez scored for Kerala Blasters
NorthEast United have endured a wretched run so far, slipping to the bottom of the table.
Ogbeche scored in the third and 60th minute to take his tally to 14 goals this season and overall number to 49, one more than Sunil Chhetri and Ferran Corominas.
Kerala-based player Mohammed Irshad hit a 79th minute equaliser for NorthEast United.
Chennaiyin have now jumped to third place from seventh with 18 points from 12 matches while NorthEast United remain at the foot of the table having collected just nine points from 13 games.
Daniel Lalhlimpuia opened the scoring for Odisha in the 17th minute.