A brilliant defensive performance from Ivan Gonzalez and some crucial saves from goalkeeper Dheeraj Singh Moirangthem were enough for Goa to get the point they needed.
Doubles from two Indian youngsters Paul Ramfangzauva (49th minute, 66th) and Jerry Mawihmingthanga (51st, 67th) enabled Odisha to end the season on a high, with S Lalhrezuala (33rd) and Diego Mauricio (69th) chipping in.
A win or a draw against Kerala will stretch NorthEast's unbeaten run under Jamil to nine games.
Kerala are without a win in their last seven league games.