Narzary smashed the ball past Sandip Nandy in a brilliant 33rd minute strike to help Dempo bag their first win from six matches.
There was a setback for Dempo who were reduced to 10-man when Jewel Raja was sent off following a second yellow, but the Goans had sealed the issue by then.
Dempo had last won against defending champions Churchill Brothers in a round nine fixture slipping to the bottom-half, but the win took them to seventh place with 16 points from 14 matches.
Putting up an unchanged line-up with Odafa and Christopher Chizoba up front, Mohun Bagan had the first move when Kastsumi Yusa got an opening early on, but the Japanese recruit was wayward.
Referee C Srikishna found himself in the centre of controversy ruling out a penalty appeal from the home side after Narayan Das used his arm to block a Ram Malik cross inside the box in the 11th minute.
In the later part of the second-half, Mohun Bagan had a flurry of chances with Odafa and Katsumi missing some easy ones as they failed to find an equaliser.
