The green-and-maroon brigade had an uninspiring start as they forgot to switch to white jersey against a team with similar colours leading to a confusion and a delay for about 20 minutes.
Mohun Bagan then carried their poor start on to the field as Dudu Omagbemi missed a flurry of chances before Army's Jain P sealed the issue with a brilliant 49th minute left-footer.
29-time champions Mohun Bagan, who last won the local league in 2009, now have a five-point deficit against leaders and defending champions East Bengal (13) with five matches in hand.