Trailing the Porcupines by a point going into the fixture that was postponed from matchday one, goals from Awudu Tahiru and Kalibo Dedy Toussaint secured all three points for the Yellow and Mauves, after Solomon Obilitey Commey put The Blues in the lead.
The victory has taken Medeama two points clear at the top of the table, while Chelsea sit second from bottom.
The game was played in Obuasi due to a home ban on The Blues' Golden City Park in Berekum for hooliganism.
Commey put Chelsea in the lead in the 27th minute before Tahiru hit back for the away side five minutes later.
Two minutes to half-time, Medeama went ahead as Toussaint netted what turned out the match winner.
Medeama face Eleven Wonders in their next game on Sunday, same day Chelsea take on Ashanti Gold in Obuasi.