Wa All Stars were holding out for a draw at the Gyamfi Park in Bekwai when a New Edubiase scored in the final minute of injury time to win 1-0 on Sunday.
Bernard Ofori nodded in a cross past goalkeeper Robert Dabou in the 94th minute to hand Edubiase all the three points.
Edubiase are now off the bottom ranks of the table as they plan their trip to Golden City Park to meet Berekum Chelsea next.