A first-half penalty by striker Josimar Martins in the 35th minute proved to be the difference between the two sides.
With this loss Mumbai FC dropped to tenth place with 7 points while the hosts rise up to seventh place with 10 points.
Coach Khalid Jamil made two changes to the team bringing in Manuel D'Souza and Haroon Amiri in place of Subhas Chakraborty and the suspended Ashutosh Mehta.
It was Mumbai FC who almost took the lead in the second minute. Mohammedan midfielder Sandeep Sangha almost scored an own goal while trying to clear Nicholas Rodrigues' freekick; however an alert Ashok Singh tipped over.
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The hosts were awarded a penalty five minutes past the half-hour mark, when defender Ritesh Perambra handled inside the box. Josimar converted from the spot to give Mohammedan the lead going into the break.
Mumbai FC almost equalised two minutes after the break. Striker Sandjar Ahmadi's shot just about went over the crossbar from close range.
The hosts thereafter kept pressing. On the other hand, Mumbai FC were restricted to few counter attacks.