Prabir Das's 24th minute goal gave Bagan a lead, before strikes by Anthony Wolfe (65th) and Chesterpoul Lyndoh (74th) took Churchill Brothers to victory.
With second successive win, Churchill Brothers' tally rose to 12 points from 12 matches, putting them in the sixth place.
Mohun Bagan who suffered their first defeat remained in the third place with 21 points from 10 matches, six points behind the table-topper East Bengal who have played two matches more.
Play was interrupted in the 80th minute after floodlights went off and there was a total black-out. Referee R Venkatesh restarted the play after 40 minutes when the floodlights came back on.
Churchill Brothers retained the team that played against DSK Shivajians in their last outing and won.
Image: Action between Churchill and Mohun Bagan
Photograph: AIFF Media