Welshman Jonathan Brown (21st) put the five-time Bangladesh Premier League champions ahead following a flurry of attacks that resulted in six corners in the first 11 minutes.
But the visitors failed to keep the momentum as Mohun Bagan stepped up near the half time with goals from Jeje Lalpekhlua (45+1st) and Balwant Singh (48th).
The Mohun Bagan forward, Singh, was in his element as he also brilliantly assisted their ace Haitian player Sony Norde (87th) to complete a fine win at the Rabindra Sarobar Stadium.
The win has given some much-needed momentum to Mohun Bagan ahead of the return leg I-League derby against East Bengal in Siliguri on Sunday.
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In title contention for the I-League title, Mohun Bagan were expected to bench their top players, but Sanjoy Sen surprised everyone by starting with both Katsumi Yusa and Norde.
Playing with two foreigners in Brown and forward Emeka Darlington, the Sky Blues started off the block with a flurry of attacks but they could not capitalise till Brown put them ahead.
Balwant set up the goal playing a pass to Norde before Jeje took the possession and scored with a left-footer.
Minutes after the changeover, Katsumi got past his marker with a diagonal run into the box and released Balwant, who ran in and scored with a powerful left-footer that went over Mohammad Sahidul Alam's head.
Mohun Bagan also missed two opportunities, first in the 66th minute following a fine run by substitute Prabir Das but his shot missed the target and hit the side-net.
Mohun Bagan take on Maldives Premier League champions Maziya Sports & Recreation in their next AFC Cup encounter at home on April 19.