The result meant ninth-placed Kerala are now level on points with SC East Bengal, who have a game in hand.
It was Odisha, which started better, enforcing a corner in the third minute but Kerala scored the opener much against the run of play.
Celtic hammered Kilmarnock 6-0 away to clinch the Scottish league title on Saturday and end the three-year reign of Glasgow rivals Rangers, who were deducted 10 points in February for entering financial administration.
FC Goa took the lead through Igor Angulo (20th minute) and Redeem Tlang (23rd) before Suresh Wangjam (33rd) reduced Bengaluru's deficit.
Khalid Jamil also created history by becoming the first Indian to coach three or more league games and guide a side to the playoffs.
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.
Late Varane header earns stuttering Man Utd 1-0 win over Wolves
With one point from the match, the Highlanders are placed joint second with ATK Mohun Bagan on 10 points
Liverpool took a giant step towards their first title in 24 years with a 3-2 win at a plucky Norwich City on Sunday, opening up a five point lead over second-placed Chelsea with three matches remaining.
B catching Wasim Jaffer on Day 1 of the third Test against South Africa, Kallis completed his 100 catches in Test cricket.
Despite a splurge of summer spending of more than 500 million pounds and counting, it was a free transfer from France who provided one of the standout moments of the Premier League's big kickoff.
Images from Saturday's action in the English Premier League.
All the results from the I-League and ISL matches played on Sunday
After all these years, Jaws still taps into the nightmares, says Raja Sen.