The India skipper was brought down late in the first half inside the rival penalty box by Balwant Singh and calmly converted the penalty kick awarded to his side in the 43rd minute.
The star striker then was in perfect position to chip in a superb centre sent by Udanta Singh, following a scorching run on the right flank, to make it 2-0 in the 52nd minute.
Mumbai got a consolation goal after a run down the middle of the field in the 72nd minute through second half substitute Leo Costa off a pass from striker Balwant Singh.
The comprehensive victory, their seventh overall, after a shock loss to struggling Delhi Dynamos pitch-forked Bengaluru over Chennaiyin FC onto the top of the table with 21 points and dumped fifth-placed Mumbai to their second straight defeat at home and fifth overall from 11 outings.
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The India captain was brought down inside the box by rival striker Balwant who had a generally poor game and was also booked for elbowing Bengaluru midfielder Harmanjot Singh.
Chhetri, who did not get many other chances to score in this period of play, beat Amrinder Singh under the Mumbai bar with a penalty kick which shook the underside of the bar and squeezed in.
He could have scored twice more after his 43rd minute strike in the first half but first shot wide on the run into the box and then blasted over the bar in quick succession. Prior to Chhetris goal, the two teams muffed quite a few chances to score.
Balwant returned the compliments for the home side by blasting over the cross piece off a square pass from Cameroonian Achille Emana who himself booted two powerful shots over the bar.
The Bengaluru midfield then took control of the proceedings but just could not get things right at the rival goal end.
Nicolas Fedor (Miku) laid a brilliant goalmouth centre which went waste and then Chhetris stiff effort off Udanta Singh's assist was blocked by Amrinder.
Mumbai too missed a few chances with Abinash Ruidas unable to beat Gurpreet Sandhu under the visiting teams bar after being fed by Sehnaj Singh, back in the team after serving out a two-game ban.
But the two strikes by Chhetri on either side of the half seemed to have taken the stuffing out of the home side and Miku's free-kick goal, after he had been brought down on the edge of the box added to the home teams misery.
Bengaluru relaxed a bit after the ninth goal of the competition by Miku which enabled Mumbai to hit back and reduce the margin.
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