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.
Bengaluru opened the scoring from the penalty spot.
Balwant Singh brought down Chhetri inside the Mumbai penalty box with a push from behind. The referee had no hesitation in awarding the visitors a penalty.
Chettri took on the responsibility, and calmly slotted the ball past Mumbai goalkeeper Amrinder Singh.
Before Chhetri gave his side the lead, Bengaluru were struggling to deal with Achille Emana, who made a few threatening runs from the midfield.
Mumbai created a few chances for themselves in a feisty first half, one of which fell to Balwant. In the 35th minute, Everton Santos' cross from the right found Balwant but his header was well saved by Bengaluru goalkeeper Gurpreet Singh.
Just before conceding the penalty, Balwant could have been sent off after he swung his elbow at Harmanjot Khabra, who went tumbling down.
The referee, however, took a lenient view of the incident, and the forward escaped with just a yellow card to his name.
Five minutes after the restart, Miku had a great opportunity to put the visitors two-up. The Spaniard was clear on goal with just Amrinder Singh to beat but he put his shot inches wides of the post.
But that didn't matter much, barely minutes later, Chhetri was again on hand to score his seventh goal of the season and double his side's advantage.
After a driving run past Mumbai FC defenders, Udanta Kumam Singh found the Indian captain in the box and side-footed shot ended in the right-hand corner of the home sides goal.
Miku then sealed the result with Bengaluru FC third goal at the hour mark. A clumsy challenge just outside his own box by Gerson Vieira on the Spaniard gave the away side free kick. And this time, Miku made no mistake. His low driven shot was too hot for Amrinder Singh.
Leo Costa, who had come on as a substitute then gave Mumbai FC a flicker of hope with a goal in the 76th minute.
After some good play with Balwant, Costa managed to slip the ball through to the Bengaluru goalkeeper. But in the time that was left on the clock, Mumbai failed to do any further damage.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
