The match, which was played at the Baba Yara Stadium in Kumasi, was seen as a must-win for the home team as they were hoping to move back into the top four of the league table.
However, things did not go according to plan for the Porcupine Warriors as they were outplayed by a determined Medeama side.
The visitors took the lead in the 15th minute through Jonathan Sowah, who scored a brilliant goal to put his team ahead.
Kotoko tried to respond, but they were unable to break through the Medeama defence.
In the second half, Kotoko continued to press forward in search of an equalizer, but they were caught on the counter-attack by Medeama.
Vincent Atingah made it 2-0 from the penalty spot in the 78th minute, after a Kotoko defender had handled the ball in the penalty area.
Despite the best efforts of Kotoko, they were unable to find a way back into the game and Medeama held on for an impressive victory.
The result means that Kotoko now find themselves in seventh place in the league table, six points behind leaders Aduana Stars.
Medeama, on the other hand, have moved up to fourth place, just three points behind the leaders, and have boosted their own title bid with this important win.