The Yellow and Mauves, have had difficulties in replicating their impressive continental form in the local league and had suffered humiliating defeats in recent times.
It came as little surprise, when Benjamin Bature shot the home side into the lead in the 28th minute the first half.
In spite of the lead, the Medeama lads probed for more goals, but the goalkeeper of Wa All Star, Richard Ofori, made some brilliant saves, to deny the home side from increasing the tally.
Although All Stars pushed more men forward to find an equalizer but their efforts proved unsuccessful.
The win would push Medeama away from the relegation zone and boost their confidence ahead of the play-off against Mamelodi Sundown of South Africa in the Confederation of Africa Football, Confederation Cup first leg encounter.
By Godwill Arthur-Mensah, GNA