Chhetri (43rd, 52nd minutes) scored on either side of the break while Venezuelan import Nicolas Fedor (63rd) rounded off the tally.
Leo Costa reduced the margin for the hosts in the 76th minute.
Bengaluru have thus climbed to the top of the league table with 21 points from 11 matches.
They are a point ahead of second placed Chennaiyin FC who have played 10 matches.
Mumbai continue to be at the fifth spot with 14 points from 11 matches.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
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