In what was a fiercely contested game in the midfield, the teams struggled to carve out clear-cut chances, but the visitors, who produced the better output in the final third, found the breakthrough through Udanta Singh in the 62nd minute.
However, in dramatic fashion, Goa's Ferran Corominas won a penalty in injury time and converted it himself to salvage a point for his team.
The result saw FC Goa join Mumbai City FC and NorthEast United FC at the top of the table with four points from two games, while Bengaluru have now played out a second straight draw.
The goalkeepers were called into action within the first 10 minutes of an intriguing game. Corominas played a good ball forward to Manvir Singh who released Seiminlen Doungel behind the Bengaluru defence with a clever through-ball. But goalkeeper Gurpreet Singh Sandhu rushed off his line just in time to collect the ball.
At the other end, Udanta Singh's looping cross from the right was punched away by Goa custodian Mohammed Nawaz.
The teams resorted to a cautious approach when going forward after the early hustle. Bengaluru had more of the ball than the home side but chances were few and far between in the goalless first half.
Hosts FC Goa enjoyed a period of dominance after the break, with the likes of Ahmed Jahouh and Ferran Corominas getting slightly more time on the ball.
But Goa couldn't score during the period they were on top and Bengaluru handed out the punishment in the 62nd minute. Udanta collected a simple flick from Manuel Onwu at the edge of the box, outfoxed Mourtada Fall with a sublime touch and slotted the ball past Nawaz to put the visitors ahead.
There was drama right at the end. With Bengaluru on the verge of victory, a clumsy challenge by Ashique Kuriniyan on Corominas after the youngster lost the ball resulted in the referee pointing to the spot. Corominas converted coolly from 12 yards to send the home supporters into delirium and earn a point for his team.
( With inputs from IANS )