After a barren first half, Mumbai, who did well to defend their citadel in the second half, scored through Essien Orok (46th) and Climax Lawerence (87th).
The win took Mumbai FC to five points from three matches, while Churchill Brothers, who suffered their second defeat, have one point from three matches.
Churchill Brothers made a couple of changes from their last match with keeper Lalit Tapa playing his first match in place of injured Arindam Bhattacharya and Anthony Periera, who has been loaned from Mohun Bagan after he refused to play them because of pay cut.
Both the teams fought evenly in the first half as the ball moved to and fro with neither team able to break the deadlock in the barren first half.
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Churchill Brothers, who enjoyed a better ball possession, pressed hard to score but Antchouet and Balwant Singh effort went out.
However, their effort bore fruit as they earned a penalty five minutes before the interval when Nicholas Rodrigues brought down Bineesh Balan inside the box and referee M B Santosh awarded penalty.
Henri Antchouet, who took the kick, directed a feeble shot at the goal which rival keeper Kunal Sawant dived to his left and managed to prevent the ball going into the net.