Second half strikes from substitute Thongkhosiem Haokip (72nd minute) and winger James Meyer (81st) handed Pune FC full three points.
The visitors were reduced to 10 men after defender Celestine Anyiche received marching orders after being shown second yellow card in the 53rd minute.
With this win Pune FC jump back to the second place with seven points from three games while Mohun Bagan dropped to 10th position with two points from three games.
The hosts went on the offensive straight from the word go and had attempts from midfielders Douhou Pierre and Arata Izumi blocked by the Bagan defence.
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Both sides thereafter settled into the game and kept on pushing for the opener. The hosts went close in the 28th minute when defender Gurjinder Kumar's brilliantly chipped cross into the box from the left found Fabiani, whose volley went just wide.
Seven minutes past the half-hour mark, Bagan went close through striker Eric Muranda. Playmaker Yusa Katsumi's freekick from the left flank was flicked on by the Pune FC defense and found Eric at the far post.