Goa were reduced to 10 men in the second half after Ivan Gonzalez received marching orders following two yellow cards within a span of seconds.
It was Odisha, which started better, enforcing a corner in the third minute but Kerala scored the opener much against the run of play.
Vicuna rang in five changes to the side that drew against SC East Bengal while Hyderabad made two changes with Liston Colaco returning to the starting eleven.
With one point from the match, the Highlanders are placed joint second with ATK Mohun Bagan on 10 points
All the results from the I-League and ISL matches played on Sunday
Here is the round-up of all the football action across Europe on the weekend
Higuain had a disappointing Copa America tournament in July, scoring two goals during the competition and missing his spot kick as Argentina lost on penalties to Chile in the final.
Carlos Tevez has been included in the squad for the first time in three years for next month's friendlies in England against Croatia and Portugal.