Goals from Abdul Fatawau Safiu and returnee Sogne Yacouba gave the Porcupines a deserved win.
After a goalless first half, Yacouba finished off an in swinger from Fatawu Safiu with a simple touch into the lower bottom corner.
Safiu, who has been Kotoko's main man in the absence of Yacouba, then sealed the win in added time.
The win takes Kotoko to the top of Premier A table on 21 points while Medeama have dropped to third ahead of the final round of matches in the group stage.
Elsewhere at the Tema sports stadium, WAFA's slump continued as Inter Allies brushed them off after a 4-2.
Full Results
INTER ALLIES 4-2 WAFA
DWARFS 1-2 LIBERTY
HEARTS 3-1 ELMINA SHARKS
KARELA 2-0 DREAMS FC
11 WONDERS 0-0 ADUANA
ASHGOLD 4-0 BECHEM UTD
KOTOKO 2-0 MEDEAMA