After both teams failed to break the deadlock in a barren first half, Sporting came back strongly in the second session to score through Man of the Match Odafe in the 70th and 87th minutes.
Katsumi Yusa pulled one back for the visitors in the 73rd minute.
The win is very important for Sporting as they now moved above Dempo FC with 17 points from as many matches, the same as Shillong Lajong, Salgaocar FC and Mumbai FC, but are placed 10th owing to inferior goal difference.
Coming off a draw and a defeat, Mohun Bagan knew the importance of a positive result today to keep themselves three points clear of their nearest rival Bengaluru FC.
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They started well and controlled the proceedings for a better part of the first half, and also had an early chance to forge ahead in the sixth minute, but a diving Ravi Kumar did well to deny Balwant Singh, who received a pass from Pierre Boya inside the box.
Sony Norde, who was a constant threat to the rival defense, saw his curling free kick put out in time by keeper Ravi Kumar.
In the second half, Pierre Boya had a glorious chance to put his team ahead off a Sony Norde pass, but his shot was blocked by Kumar.
Sporting took the lead when a combined move on the right between Pratesh Shirodkar and Brendon Fernndes saw the latter sending a curling lob into the goal for Odafe to head home.