Medeama, who had defeated Ebusua Dwarfs 6-5 in the opening fixture of this season's curtain raiser competition, started the game brightly as they dictated the pace of the encounter.
Their dominance over the Phobians was telling as they created two quick opportunities, only for goalkeeper Ben Mensah to come to the rescue of the timid Accra-based giants.
Hearts raised their performance level but were pegged back by Kwame Boateng's 16th minute strike to the chagrin of their boisterous fans after a school boys error by defender Richard Akrofi.
The Yellow and Mauves quickly extended their advantage in the 23rd minute through Agyenim Boateng after he was put through by striker Kwame Boateng.
The Phobians did all they could to get back into the game in the second stanza with the introduction of Patrick Razak but their incessant efforts did not yield any result as Medeama held on to collect the maximum points.
Hearts can still qualify for the semifinal if they record positive result against Ebusua Dwarfs in their last game.