Youngster Nana Kofi Babil opened the scoring in the first half to increase his goal tally to four.
After the break, Prince Opoku Agyemang doubled the lead for the visitors and it was his 8th goal of the season.
Victorien Adebayor the marksman for Inter Allies pulled one back for the hosts to take his goal tally to 11 as the leading goal scorer in the Ghana Premier League.
The win is Medeama’s first victory at Inter Allies in five visits.
Prince Yaw Owusu was adjudged the man of the match.