The goals were scored by Edu Garcia and Dimas Delgado Morgado in the 35th and 82nd minutes, respectively.
The hosts also are on the verge of creating ISL history -- if they win their next match against Pune FC it will be a record sixth on the trot.
Though Goa passed the ball around and dominated possession for the first half an hour, Bengaluru who were chasing the ball in hope of forcing errors from their rivals, got their act together gradually.
Bengaluru tasted first blood when Toni Dovale sent a corner-kick into the centre of the box where Garcia rose to send a looping header into the top corner of the post.
Bengaluru sealed the game in their favour with the second goal after Garcia broke forward on the counter and brought the ball into the centre. Toni Dovakke headed it into the path of Dimas who slotted the ball past a hapless Naveen Kumar.
In the 23rd minute, skipper Suni Chhetri met a corner with his head at the near post but sent it over the bar. In the next minute, Nishu Kumar ran towards the byline on the left before cutting the ball back for Haokip at the near post, who flicked the ball but it was well saved by Naveen.
In the 33rd minute, Garcia tried to score but the shot was too hard and flew over Naveen, who watched it sailing over the bar.
In the next minute, Chettri sent a dangerous ball from the left and Pinheiro cleared it for a corner.
In the 71st minute, Dimas sent a corner into the centre where John Johnson headed it straight into the hands of Naveen.
Goa made their first move in the sixth minute through the combination of Mandar Rao Dessai's cross and Ferran Corominas' header, but it was brilliantly saved by Gurupreet Sandhu.
Again in the 10th minute, Goa had a close chance as Manvir cut in from the right and sent a powerful shot at goal, forcing Gurpreet to dive to his left.
Mandar again, in the 12th minute, got the better of Bheke on the left flank and sent a cross that was too close for Gurpreet, but he collected the ball safely.
Lanza then aimed at the BFC post from a free kick but that was parried away by an alert Gurupreet in the 20th minute.
In the 75th minute, Corominas got an opportunity through a corner when Gurupreet fumbled initially but saved it later.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)