Starting as underdogs, Mohun Bagan looked a reformed side with Odafa striking in the 30th and 80th minutes, for the Nigerian's tally to only three this season.
Ram Malik (75th) struck in between to complete their rout of Pune FC. This was Mohun Bagan's fourth win this season and the crucial three points helped them jumped to 18 points from 15 matches.
The visitors looked to attack up front with comeback man Izumi Arata making inroads but his attempt was not enough with his leftfooter missing the target.
In the 23rd minute, Pune FC once again had a failed attempt with Mustapha Riga setting up Douhou Pierre who only managed to shoot wide outside the box.
But it was Odafa who made his presence felt when Arata failed to clear a corner as new recruit Christopher Chizoba set up his Nigerian compatriot to take Mohun Bagan ahead with an easy shot.
Goalkeeper Shilton Paul too was outstanding with a diving save from Riga in the second half while Odafa was in his elements after scoring his only second goal this season.
Mohun Bagan doubled the lead capitalising on a defensive lapse by Pune as Malik doing the formality.
Haokip pulled one back for his side as he slotted the ball into an empty net while Odafa completed his brace battling against two defenders.
In fact, Odafa could have easily struck a hattrick but his shot hit the cross bar minutes before scoing the double.