The Phobians picked up a point in midweek and needed to win this game to keep their hopes of defending the league title alive.
Coach Samuel Boadu and his team needed this win to keep the chase with leaders Asante Kotoko on the table.
The two sides created a lot of chances but were unable to score in the first half.
Obeng Jnr came close to scoring for Hearts after a defensive mistake from the medeama defense. His kick was too shallow to beat Anaba in the 33rd minute.
Hearts of Oak appealed for a penalty in the 50th minute after the ball struck the hand of Medeama defender Vincent Atinga in the box. Referee Fuseini Alfaa Ba-Adey ignored for play to continue.
Isaac Mensah broke the deadlock for Hearts of Oak in the 55th minute with a nice header from a Daniel Afriyie Barnieh cross.
The defending league champions held onto the lead to secure the win at the Accra Sports Stadium.