Nigerian-born Indonesian international Greg Nwokolo gave Madura the lead in the 21st minute after he was set up by Odemwingie.
In three minutes of added time in the first half, Odemwingie also provided the assist for Fachrudin Aryanto who made it 2-0.
In the 54th minute, Rizky Rizal Ripora pulled a goal back for Barito Putera bringing the score to 2-1.
But in the 65th minute, Odemwingie got amongst the goals to extend Madura’s lead and secure the win.
Osaze has now scored 15 goals in 22 league appearances for Madura so far this season.
Madura are now fourth on 60 points, just three points adrift of leaders Bhayangkara FC.