Mohun Bagan took the lead as Yusa Katsumi scored off a penalty in the 37th minute but the home side pumped in twice in the second half to emerge winners in the first leg of the home and away tie.
Bengaluru, who had finished runners-up in the tournament last season, found their equaliser in 52nd minute as Jhingan, off a clearance from Cameron Watson's corner, shot the ball home with Shilton Paul stranded.
Chhetri scored the match-winner in the 58th minute off a free-kick as the ball hit the bottom corner of the net leaving a hapless Mohun Bagan goalkeeper Paul stranded.
Mohun Bagan were awarded the penalty after their striker Sony Norde was brought down by Jhingan inside the box. Yusa stepped up to send a low shot to Aridam Bhattacharya's left and hit the net despite the keeper's slight touch.
The second half completely belonged to Bengaluru as Albert Roca's team pumped in two goals. Chances also came their way after their second goal.
The hosts had close chances in the 62nd, 66th, 69th, 72nd, 78th 82nd and in fourth minute of the injury time.
For Mohun Bagan, it was a nightmare of a match as Yusa picked up an injury and was stretchered off the field, which did not help the team.
The Mohun Bagan midfield duo did an excellent job as Bikramjit Singh and Sehnaj had fortified the region and let nothing pass through them.
In the 11th minute, Mohun Bagan wasted a golden opportunity when Yusa sent a lovely pass to Jeje Lalpekhlua, who needed to just touch it but could not and Jhingan ran to clear the ball.
The return leg of the tie will be played in Kolkata on May 17.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)