Substitute Manish Bhargav (53rd minute) scored the only goal of the game early in the second half to hand all three points to the visitors.
The visitors were reduced to ten-men deep into the second half injury time after medio Sankar Oraon received his second yellow.
With this win, Mohun Bagan jump up to seventh place with 8 points from six games while the hosts go down to ninth place with 6 points from seven games.
Coach Khalid Jamil made one change to the team that faced Shillong Lajong in the previous round, replacing medio Dane Pereira with Manuel D'Souza.
In a game of equal exchanges, it was the visitors who went close first inside ten minutes. Striker Sabeeth Sathyan created space after a failed clearance and let fly from inside the box.
However, custodian Kunal Sawant came up with a brilliant block to deny him.
At the other end, Mumbai FC went agonisingly close six minutes later.
Striker Sandjar Ahmadi floated freekick in from the left was almost headed into his own net by Bagan defender Kingshuk Debnath.
Thereafter both sides were engaged in a midfield battle and failed to break the deadlock and went into the break tied at goalless.
The visitors went close moments after restart only to be denied by Sawant once again. After Yusa Katsumi got into the clear on the left, he sent in a low cross for Sabeeth inside the box. Sawant sensed the danger and produced a diving block to deny the Bagan striker.
Bagan took the lead against the run of play eight minutes later. First-half substitute Bhargav - on for Nicolau Borges - headed in defender Pritam Kotal's cross from the right past the helpless Mumbai FC custodian.
Midway through the half, Mumbai FC went close through striker Sandjar. The Afghan international went into the clear on a counter, but his low shot from the right went wide at the far post.
The hosts kept pressing for the equaliser but poor finishing in the final third let them down. Skipper Nicholas Rodrigues and Sandjar had their freekicks saved by Bagan custodian Shilton Paul late in the second half.
The visitors held on to their slender lead to secure their second win of the campaign.
--IBNS (Posted on 26-10-2013)