The Phobians scored a goal in each half. Ibrahim Salifu scored the first with his head then Agyenim Boateng secured victory with a superb inside the box strike.
Although it is a good advantage for Hearts, they would be disappointed not to score the vital third as their opponents played the last 17 minutes with 10 men.
The second leg will be played next week with any kind of draw enough to take Hearts of Oak through.
Watch highlights of the match below